diff --git a/doc/api/next_api_changes/development/30143-ES.rst b/doc/api/next_api_changes/development/30143-ES.rst
new file mode 100644
index 000000000000..2d79ad6bbe9d
--- /dev/null
+++ b/doc/api/next_api_changes/development/30143-ES.rst
@@ -0,0 +1,7 @@
+Glyph indices now typed distinctly from character codes
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Previously, character codes and glyph indices were both typed as `int`, which means you
+could mix and match them erroneously. While the character code can't be made a distinct
+type (because it's used for `chr`/`ord`), typing glyph indices as a distinct type means
+these can't be fully swapped.
diff --git a/lib/matplotlib/_afm.py b/lib/matplotlib/_afm.py
index 352d3c42247e..3d7f7a44baca 100644
--- a/lib/matplotlib/_afm.py
+++ b/lib/matplotlib/_afm.py
@@ -30,9 +30,10 @@
 import inspect
 import logging
 import re
-from typing import BinaryIO, NamedTuple, TypedDict
+from typing import BinaryIO, NamedTuple, TypedDict, cast
 
 from ._mathtext_data import uni2type1
+from .ft2font import CharacterCodeType, GlyphIndexType
 
 
 _log = logging.getLogger(__name__)
@@ -197,7 +198,7 @@ class CharMetrics(NamedTuple):
     The bbox of the character (B) as a tuple (*llx*, *lly*, *urx*, *ury*)."""
 
 
-def _parse_char_metrics(fh: BinaryIO) -> tuple[dict[int, CharMetrics],
+def _parse_char_metrics(fh: BinaryIO) -> tuple[dict[CharacterCodeType, CharMetrics],
                                                dict[str, CharMetrics]]:
     """
     Parse the given filehandle for character metrics information.
@@ -218,7 +219,7 @@ def _parse_char_metrics(fh: BinaryIO) -> tuple[dict[int, CharMetrics],
     """
     required_keys = {'C', 'WX', 'N', 'B'}
 
-    ascii_d: dict[int, CharMetrics] = {}
+    ascii_d: dict[CharacterCodeType, CharMetrics] = {}
     name_d: dict[str, CharMetrics] = {}
     for bline in fh:
         # We are defensively letting values be utf8. The spec requires
@@ -409,19 +410,21 @@ def get_str_bbox_and_descent(self, s: str) -> tuple[int, int, float, int, int]:
 
         return left, miny, total_width, maxy - miny, -miny
 
-    def get_glyph_name(self, glyph_ind: int) -> str:  # For consistency with FT2Font.
+    def get_glyph_name(self,  # For consistency with FT2Font.
+                       glyph_ind: GlyphIndexType) -> str:
         """Get the name of the glyph, i.e., ord(';') is 'semicolon'."""
-        return self._metrics[glyph_ind].name
+        return self._metrics[cast(CharacterCodeType, glyph_ind)].name
 
-    def get_char_index(self, c: int) -> int:  # For consistency with FT2Font.
+    def get_char_index(self,  # For consistency with FT2Font.
+                       c: CharacterCodeType) -> GlyphIndexType:
         """
         Return the glyph index corresponding to a character code point.
 
         Note, for AFM fonts, we treat the glyph index the same as the codepoint.
         """
-        return c
+        return cast(GlyphIndexType, c)
 
-    def get_width_char(self, c: int) -> float:
+    def get_width_char(self, c: CharacterCodeType) -> float:
         """Get the width of the character code from the character metric WX field."""
         return self._metrics[c].width
 
diff --git a/lib/matplotlib/_mathtext.py b/lib/matplotlib/_mathtext.py
index 19ddbb6d0883..4ebe09cbc311 100644
--- a/lib/matplotlib/_mathtext.py
+++ b/lib/matplotlib/_mathtext.py
@@ -37,7 +37,8 @@
 
 if T.TYPE_CHECKING:
     from collections.abc import Iterable
-    from .ft2font import Glyph
+    from .ft2font import CharacterCodeType, Glyph, GlyphIndexType
+
 
 ParserElement.enable_packrat()
 _log = logging.getLogger("matplotlib.mathtext")
@@ -47,7 +48,7 @@
 # FONTS
 
 
-def get_unicode_index(symbol: str) -> int:  # Publicly exported.
+def get_unicode_index(symbol: str) -> CharacterCodeType:  # Publicly exported.
     r"""
     Return the integer index (from the Unicode table) of *symbol*.
 
@@ -85,7 +86,7 @@ class VectorParse(NamedTuple):
     width: float
     height: float
     depth: float
-    glyphs: list[tuple[FT2Font, float, int, float, float]]
+    glyphs: list[tuple[FT2Font, float, GlyphIndexType, float, float]]
     rects: list[tuple[float, float, float, float]]
 
 VectorParse.__module__ = "matplotlib.mathtext"
@@ -130,7 +131,7 @@ def __init__(self, box: Box):
     def to_vector(self) -> VectorParse:
         w, h, d = map(
             np.ceil, [self.box.width, self.box.height, self.box.depth])
-        gs = [(info.font, info.fontsize, info.num, ox, h - oy + info.offset)
+        gs = [(info.font, info.fontsize, info.glyph_id, ox, h - oy + info.offset)
               for ox, oy, info in self.glyphs]
         rs = [(x1, h - y2, x2 - x1, y2 - y1)
               for x1, y1, x2, y2 in self.rects]
@@ -212,7 +213,7 @@ class FontInfo(NamedTuple):
     fontsize: float
     postscript_name: str
     metrics: FontMetrics
-    num: int
+    glyph_id: GlyphIndexType
     glyph: Glyph
     offset: float
 
@@ -365,7 +366,7 @@ def _get_offset(self, font: FT2Font, glyph: Glyph, fontsize: float,
         return 0.
 
     def _get_glyph(self, fontname: str, font_class: str,
-                   sym: str) -> tuple[FT2Font, int, bool]:
+                   sym: str) -> tuple[FT2Font, CharacterCodeType, bool]:
         raise NotImplementedError
 
     # The return value of _get_info is cached per-instance.
@@ -373,7 +374,8 @@ def _get_info(self, fontname: str, font_class: str, sym: str, fontsize: float,
                   dpi: float) -> FontInfo:
         font, num, slanted = self._get_glyph(fontname, font_class, sym)
         font.set_size(fontsize, dpi)
-        glyph = font.load_char(num, flags=self.load_glyph_flags)
+        glyph_id = font.get_char_index(num)
+        glyph = font.load_glyph(glyph_id, flags=self.load_glyph_flags)
 
         xmin, ymin, xmax, ymax = (val / 64 for val in glyph.bbox)
         offset = self._get_offset(font, glyph, fontsize, dpi)
@@ -395,7 +397,7 @@ def _get_info(self, fontname: str, font_class: str, sym: str, fontsize: float,
             fontsize=fontsize,
             postscript_name=font.postscript_name,
             metrics=metrics,
-            num=num,
+            glyph_id=glyph_id,
             glyph=glyph,
             offset=offset
         )
@@ -425,7 +427,8 @@ def get_kern(self, font1: str, fontclass1: str, sym1: str, fontsize1: float,
             info1 = self._get_info(font1, fontclass1, sym1, fontsize1, dpi)
             info2 = self._get_info(font2, fontclass2, sym2, fontsize2, dpi)
             font = info1.font
-            return font.get_kerning(info1.num, info2.num, Kerning.DEFAULT) / 64
+            return font.get_kerning(info1.glyph_id, info2.glyph_id,
+                                    Kerning.DEFAULT) / 64
         return super().get_kern(font1, fontclass1, sym1, fontsize1,
                                 font2, fontclass2, sym2, fontsize2, dpi)
 
@@ -459,7 +462,7 @@ def __init__(self, default_font_prop: FontProperties, load_glyph_flags: LoadFlag
     _slanted_symbols = set(r"\int \oint".split())
 
     def _get_glyph(self, fontname: str, font_class: str,
-                   sym: str) -> tuple[FT2Font, int, bool]:
+                   sym: str) -> tuple[FT2Font, CharacterCodeType, bool]:
         font = None
         if fontname in self.fontmap and sym in latex_to_bakoma:
             basename, num = latex_to_bakoma[sym]
@@ -551,7 +554,7 @@ class UnicodeFonts(TruetypeFonts):
     # Some glyphs are not present in the `cmr10` font, and must be brought in
     # from `cmsy10`. Map the Unicode indices of those glyphs to the indices at
     # which they are found in `cmsy10`.
-    _cmr10_substitutions = {
+    _cmr10_substitutions: dict[CharacterCodeType, CharacterCodeType] = {
         0x00D7: 0x00A3,  # Multiplication sign.
         0x2212: 0x00A1,  # Minus sign.
     }
@@ -594,11 +597,11 @@ def __init__(self, default_font_prop: FontProperties, load_glyph_flags: LoadFlag
     _slanted_symbols = set(r"\int \oint".split())
 
     def _map_virtual_font(self, fontname: str, font_class: str,
-                          uniindex: int) -> tuple[str, int]:
+                          uniindex: CharacterCodeType) -> tuple[str, CharacterCodeType]:
         return fontname, uniindex
 
     def _get_glyph(self, fontname: str, font_class: str,
-                   sym: str) -> tuple[FT2Font, int, bool]:
+                   sym: str) -> tuple[FT2Font, CharacterCodeType, bool]:
         try:
             uniindex = get_unicode_index(sym)
             found_symbol = True
@@ -607,8 +610,7 @@ def _get_glyph(self, fontname: str, font_class: str,
             found_symbol = False
             _log.warning("No TeX to Unicode mapping for %a.", sym)
 
-        fontname, uniindex = self._map_virtual_font(
-            fontname, font_class, uniindex)
+        fontname, uniindex = self._map_virtual_font(fontname, font_class, uniindex)
 
         new_fontname = fontname
 
@@ -693,7 +695,7 @@ def __init__(self, default_font_prop: FontProperties, load_glyph_flags: LoadFlag
             self.fontmap[name] = fullpath
 
     def _get_glyph(self, fontname: str, font_class: str,
-                   sym: str) -> tuple[FT2Font, int, bool]:
+                   sym: str) -> tuple[FT2Font, CharacterCodeType, bool]:
         # Override prime symbol to use Bakoma.
         if sym == r'\prime':
             return self.bakoma._get_glyph(fontname, font_class, sym)
@@ -783,7 +785,7 @@ def __init__(self, default_font_prop: FontProperties, load_glyph_flags: LoadFlag
             self.fontmap[name] = fullpath
 
     def _map_virtual_font(self, fontname: str, font_class: str,
-                          uniindex: int) -> tuple[str, int]:
+                          uniindex: CharacterCodeType) -> tuple[str, CharacterCodeType]:
         # Handle these "fonts" that are actually embedded in
         # other fonts.
         font_mapping = stix_virtual_fonts.get(fontname)
@@ -1170,7 +1172,7 @@ def __init__(self, elements: T.Sequence[Node]):
         self.glue_sign    = 0    # 0: normal, -1: shrinking, 1: stretching
         self.glue_order   = 0    # The order of infinity (0 - 3) for the glue
 
-    def __repr__(self):
+    def __repr__(self) -> str:
         return "{}<w={:.02f} h={:.02f} d={:.02f} s={:.02f}>[{}]".format(
             super().__repr__(),
             self.width, self.height,
diff --git a/lib/matplotlib/_mathtext_data.py b/lib/matplotlib/_mathtext_data.py
index 5819ee743044..0451791e9f26 100644
--- a/lib/matplotlib/_mathtext_data.py
+++ b/lib/matplotlib/_mathtext_data.py
@@ -3,9 +3,12 @@
 """
 
 from __future__ import annotations
-from typing import overload
+from typing import TypeAlias, overload
 
-latex_to_bakoma = {
+from .ft2font import CharacterCodeType
+
+
+latex_to_bakoma: dict[str, tuple[str, CharacterCodeType]] = {
     '\\__sqrt__'                 : ('cmex10', 0x70),
     '\\bigcap'                   : ('cmex10', 0x5c),
     '\\bigcup'                   : ('cmex10', 0x5b),
@@ -241,7 +244,7 @@
 
 # Automatically generated.
 
-type12uni = {
+type12uni: dict[str, CharacterCodeType] = {
     'aring'          : 229,
     'quotedblright'  : 8221,
     'V'              : 86,
@@ -475,7 +478,7 @@
 #  for key in sd:
 #      print("{0:24} : {1: <s},".format("'" + key + "'", sd[key]))
 
-tex2uni = {
+tex2uni: dict[str, CharacterCodeType] = {
     '#'                      : 0x23,
     '$'                      : 0x24,
     '%'                      : 0x25,
@@ -1113,8 +1116,9 @@
 # Each element is a 4-tuple of the form:
 #   src_start, src_end, dst_font, dst_start
 
-_EntryTypeIn = tuple[str, str, str, str | int]
-_EntryTypeOut = tuple[int, int, str, int]
+_EntryTypeIn: TypeAlias = tuple[str, str, str, str | CharacterCodeType]
+_EntryTypeOut: TypeAlias = tuple[CharacterCodeType, CharacterCodeType, str,
+                                 CharacterCodeType]
 
 _stix_virtual_fonts: dict[str, dict[str, list[_EntryTypeIn]] | list[_EntryTypeIn]] = {
     'bb': {
@@ -1735,7 +1739,7 @@ def _normalize_stix_fontcodes(d):
 del _stix_virtual_fonts
 
 # Fix some incorrect glyphs.
-stix_glyph_fixes = {
+stix_glyph_fixes: dict[CharacterCodeType, CharacterCodeType] = {
     # Cap and Cup glyphs are swapped.
     0x22d2: 0x22d3,
     0x22d3: 0x22d2,
diff --git a/lib/matplotlib/_text_helpers.py b/lib/matplotlib/_text_helpers.py
index b9603b114bc2..22b52f943af6 100644
--- a/lib/matplotlib/_text_helpers.py
+++ b/lib/matplotlib/_text_helpers.py
@@ -7,14 +7,14 @@
 import dataclasses
 
 from . import _api
-from .ft2font import FT2Font, Kerning, LoadFlags
+from .ft2font import FT2Font, GlyphIndexType, Kerning, LoadFlags
 
 
 @dataclasses.dataclass(frozen=True)
 class LayoutItem:
     ft_object: FT2Font
     char: str
-    glyph_idx: int
+    glyph_index: GlyphIndexType
     x: float
     prev_kern: float
 
diff --git a/lib/matplotlib/backends/_backend_pdf_ps.py b/lib/matplotlib/backends/_backend_pdf_ps.py
index a2a878d54156..21f1e82f5956 100644
--- a/lib/matplotlib/backends/_backend_pdf_ps.py
+++ b/lib/matplotlib/backends/_backend_pdf_ps.py
@@ -20,18 +20,18 @@ def _cached_get_afm_from_fname(fname):
         return AFM(fh)
 
 
-def get_glyphs_subset(fontfile, characters):
+def get_glyphs_subset(fontfile, glyphs):
     """
-    Subset a TTF font
+    Subset a TTF font.
 
-    Reads the named fontfile and restricts the font to the characters.
+    Reads the named fontfile and restricts the font to the glyphs.
 
     Parameters
     ----------
     fontfile : str
         Path to the font file
-    characters : str
-        Continuous set of characters to include in subset
+    glyphs : set[int]
+        Set of glyph IDs to include in subset.
 
     Returns
     -------
@@ -39,8 +39,8 @@ def get_glyphs_subset(fontfile, characters):
         An open font object representing the subset, which needs to
         be closed by the caller.
     """
-
-    options = subset.Options(glyph_names=True, recommended_glyphs=True)
+    options = subset.Options(glyph_names=True, recommended_glyphs=True,
+                             retain_gids=True)
 
     # Prevent subsetting extra tables.
     options.drop_tables += [
@@ -71,7 +71,7 @@ def get_glyphs_subset(fontfile, characters):
 
     font = subset.load_font(fontfile, options)
     subsetter = subset.Subsetter(options=options)
-    subsetter.populate(text=characters)
+    subsetter.populate(gids=glyphs)
     subsetter.subset(font)
     return font
 
@@ -97,10 +97,10 @@ def font_as_file(font):
 
 class CharacterTracker:
     """
-    Helper for font subsetting by the pdf and ps backends.
+    Helper for font subsetting by the PDF and PS backends.
 
-    Maintains a mapping of font paths to the set of character codepoints that
-    are being used from that font.
+    Maintains a mapping of font paths to the set of glyphs that are being used from that
+    font.
     """
 
     def __init__(self):
@@ -110,10 +110,11 @@ def track(self, font, s):
         """Record that string *s* is being typeset using font *font*."""
         char_to_font = font._get_fontmap(s)
         for _c, _f in char_to_font.items():
-            self.used.setdefault(_f.fname, set()).add(ord(_c))
+            glyph_index = _f.get_char_index(ord(_c))
+            self.used.setdefault(_f.fname, set()).add(glyph_index)
 
     def track_glyph(self, font, glyph):
-        """Record that codepoint *glyph* is being typeset using font *font*."""
+        """Record that glyph index *glyph* is being typeset using font *font*."""
         self.used.setdefault(font.fname, set()).add(glyph)
 
 
diff --git a/lib/matplotlib/backends/backend_cairo.py b/lib/matplotlib/backends/backend_cairo.py
index 7409cd35b394..b10431800f1f 100644
--- a/lib/matplotlib/backends/backend_cairo.py
+++ b/lib/matplotlib/backends/backend_cairo.py
@@ -8,6 +8,7 @@
 
 import functools
 import gzip
+import itertools
 import math
 
 import numpy as np
@@ -248,13 +249,12 @@ def _draw_mathtext(self, gc, x, y, s, prop, angle):
         if angle:
             ctx.rotate(np.deg2rad(-angle))
 
-        for font, fontsize, idx, ox, oy in glyphs:
+        for (font, fontsize), font_glyphs in itertools.groupby(
+                glyphs, key=lambda x: (x[0], x[1])):
             ctx.new_path()
-            ctx.move_to(ox, -oy)
-            ctx.select_font_face(
-                *_cairo_font_args_from_font_prop(ttfFontProperty(font)))
+            ctx.select_font_face(*_cairo_font_args_from_font_prop(ttfFontProperty(font)))
             ctx.set_font_size(self.points_to_pixels(fontsize))
-            ctx.show_text(chr(idx))
+            ctx.show_glyphs([(idx, ox, -oy) for _, _, idx, ox, oy in font_glyphs])
 
         for ox, oy, w, h in rects:
             ctx.new_path()
diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
index ff351e301176..187094949f5c 100644
--- a/lib/matplotlib/backends/backend_pdf.py
+++ b/lib/matplotlib/backends/backend_pdf.py
@@ -960,9 +960,9 @@ def writeFonts(self):
             else:
                 # a normal TrueType font
                 _log.debug('Writing TrueType font.')
-                chars = self._character_tracker.used.get(filename)
-                if chars:
-                    fonts[Fx] = self.embedTTF(filename, chars)
+                glyphs = self._character_tracker.used.get(filename)
+                if glyphs:
+                    fonts[Fx] = self.embedTTF(filename, glyphs)
         self.writeObject(self.fontObject, fonts)
 
     def _write_afm_font(self, filename):
@@ -1136,9 +1136,8 @@ def _get_xobject_glyph_name(self, filename, glyph_name):
 end
 end"""
 
-    def embedTTF(self, filename, characters):
+    def embedTTF(self, filename, glyphs):
         """Embed the TTF font from the named file into the document."""
-
         font = get_font(filename)
         fonttype = mpl.rcParams['pdf.fonttype']
 
@@ -1153,7 +1152,7 @@ def cvt(length, upe=font.units_per_EM, nearest=True):
             else:
                 return math.ceil(value)
 
-        def embedTTFType3(font, characters, descriptor):
+        def embedTTFType3(font, glyphs, descriptor):
             """The Type 3-specific part of embedding a Truetype font"""
             widthsObject = self.reserveObject('font widths')
             fontdescObject = self.reserveObject('font descriptor')
@@ -1200,15 +1199,13 @@ def get_char_width(charcode):
             # Make the "Differences" array, sort the ccodes < 255 from
             # the multi-byte ccodes, and build the whole set of glyph ids
             # that we need from this font.
-            glyph_ids = []
             differences = []
             multi_byte_chars = set()
-            for c in characters:
-                ccode = c
-                gind = font.get_char_index(ccode)
-                glyph_ids.append(gind)
+            charmap = {gind: ccode for ccode, gind in font.get_charmap().items()}
+            for gind in glyphs:
                 glyph_name = font.get_glyph_name(gind)
-                if ccode <= 255:
+                ccode = charmap.get(gind)
+                if ccode is not None and ccode <= 255:
                     differences.append((ccode, glyph_name))
                 else:
                     multi_byte_chars.add(glyph_name)
@@ -1222,7 +1219,7 @@ def get_char_width(charcode):
                 last_c = c
 
             # Make the charprocs array.
-            rawcharprocs = _get_pdf_charprocs(filename, glyph_ids)
+            rawcharprocs = _get_pdf_charprocs(filename, glyphs)
             charprocs = {}
             for charname in sorted(rawcharprocs):
                 stream = rawcharprocs[charname]
@@ -1259,7 +1256,7 @@ def get_char_width(charcode):
 
             return fontdictObject
 
-        def embedTTFType42(font, characters, descriptor):
+        def embedTTFType42(font, glyphs, descriptor):
             """The Type 42-specific part of embedding a Truetype font"""
             fontdescObject = self.reserveObject('font descriptor')
             cidFontDictObject = self.reserveObject('CID font dictionary')
@@ -1269,9 +1266,8 @@ def embedTTFType42(font, characters, descriptor):
             wObject = self.reserveObject('Type 0 widths')
             toUnicodeMapObject = self.reserveObject('ToUnicode map')
 
-            subset_str = "".join(chr(c) for c in characters)
-            _log.debug("SUBSET %s characters: %s", filename, subset_str)
-            with _backend_pdf_ps.get_glyphs_subset(filename, subset_str) as subset:
+            _log.debug("SUBSET %s characters: %s", filename, glyphs)
+            with _backend_pdf_ps.get_glyphs_subset(filename, glyphs) as subset:
                 fontdata = _backend_pdf_ps.font_as_file(subset)
             _log.debug(
                 "SUBSET %s %d -> %d", filename,
@@ -1319,11 +1315,11 @@ def embedTTFType42(font, characters, descriptor):
             cid_to_gid_map = ['\0'] * 65536
             widths = []
             max_ccode = 0
-            for c in characters:
-                ccode = c
-                gind = font.get_char_index(ccode)
-                glyph = font.load_char(ccode,
-                                       flags=LoadFlags.NO_SCALE | LoadFlags.NO_HINTING)
+            charmap = {gind: ccode for ccode, gind in font.get_charmap().items()}
+            for gind in glyphs:
+                glyph = font.load_glyph(gind,
+                                        flags=LoadFlags.NO_SCALE | LoadFlags.NO_HINTING)
+                ccode = charmap[gind]
                 widths.append((ccode, cvt(glyph.horiAdvance)))
                 if ccode < 65536:
                     cid_to_gid_map[ccode] = chr(gind)
@@ -1361,11 +1357,10 @@ def embedTTFType42(font, characters, descriptor):
                             (len(unicode_groups), b"\n".join(unicode_bfrange)))
 
             # Add XObjects for unsupported chars
-            glyph_ids = []
-            for ccode in characters:
-                if not _font_supports_glyph(fonttype, ccode):
-                    gind = full_font.get_char_index(ccode)
-                    glyph_ids.append(gind)
+            glyph_ids = [
+                gind for gind in glyphs
+                if not _font_supports_glyph(fonttype, charmap[gind])
+            ]
 
             bbox = [cvt(x, nearest=False) for x in full_font.bbox]
             rawcharprocs = _get_pdf_charprocs(filename, glyph_ids)
@@ -1450,9 +1445,9 @@ def embedTTFType42(font, characters, descriptor):
             }
 
         if fonttype == 3:
-            return embedTTFType3(font, characters, descriptor)
+            return embedTTFType3(font, glyphs, descriptor)
         elif fonttype == 42:
-            return embedTTFType42(font, characters, descriptor)
+            return embedTTFType42(font, glyphs, descriptor)
 
     def alphaState(self, alpha):
         """Return name of an ExtGState that sets alpha to the given value."""
@@ -2215,14 +2210,19 @@ def draw_mathtext(self, gc, x, y, s, prop, angle):
         oldx, oldy = 0, 0
         unsupported_chars = []
 
+        font_charmaps = {}
         self.file.output(Op.begin_text)
-        for font, fontsize, num, ox, oy in glyphs:
-            self.file._character_tracker.track_glyph(font, num)
+        for font, fontsize, glyph_index, ox, oy in glyphs:
+            self.file._character_tracker.track_glyph(font, glyph_index)
             fontname = font.fname
-            if not _font_supports_glyph(fonttype, num):
+            if font not in font_charmaps:
+                font_charmaps[font] = {gind: ccode
+                                       for ccode, gind in font.get_charmap().items()}
+            ccode = font_charmaps[font].get(glyph_index)
+            if ccode is None or not _font_supports_glyph(fonttype, ccode):
                 # Unsupported chars (i.e. multibyte in Type 3 or beyond BMP in
                 # Type 42) must be emitted separately (below).
-                unsupported_chars.append((font, fontsize, ox, oy, num))
+                unsupported_chars.append((font, fontsize, ox, oy, glyph_index))
             else:
                 self._setup_textpos(ox, oy, 0, oldx, oldy)
                 oldx, oldy = ox, oy
@@ -2230,13 +2230,12 @@ def draw_mathtext(self, gc, x, y, s, prop, angle):
                     self.file.output(self.file.fontName(fontname), fontsize,
                                      Op.selectfont)
                     prev_font = fontname, fontsize
-                self.file.output(self.encode_string(chr(num), fonttype),
+                self.file.output(self.encode_string(chr(ccode), fonttype),
                                  Op.show)
         self.file.output(Op.end_text)
 
-        for font, fontsize, ox, oy, num in unsupported_chars:
-            self._draw_xobject_glyph(
-                font, fontsize, font.get_char_index(num), ox, oy)
+        for font, fontsize, ox, oy, glyph_index in unsupported_chars:
+            self._draw_xobject_glyph(font, fontsize, glyph_index, ox, oy)
 
         # Draw any horizontal lines in the math layout
         for ox, oy, width, height in rects:
@@ -2399,7 +2398,7 @@ def draw_text(self, gc, x, y, s, prop, angle, ismath=False, mtext=None):
                     singlebyte_chunks[-1][2].append(item.char)
                     prev_was_multibyte = False
                 else:
-                    multibyte_glyphs.append((item.ft_object, item.x, item.glyph_idx))
+                    multibyte_glyphs.append((item.ft_object, item.x, item.glyph_index))
                     prev_was_multibyte = True
             # Do the rotation and global translation as a single matrix
             # concatenation up front
@@ -2409,7 +2408,6 @@ def draw_text(self, gc, x, y, s, prop, angle, ismath=False, mtext=None):
                              -math.sin(a), math.cos(a),
                              x, y, Op.concat_matrix)
             # Emit all the 1-byte characters in a BT/ET group.
-
             self.file.output(Op.begin_text)
             prev_start_x = 0
             for ft_object, start_x, kerns_or_chars in singlebyte_chunks:
diff --git a/lib/matplotlib/backends/backend_ps.py b/lib/matplotlib/backends/backend_ps.py
index 368564a1518d..f55d093a67bf 100644
--- a/lib/matplotlib/backends/backend_ps.py
+++ b/lib/matplotlib/backends/backend_ps.py
@@ -88,16 +88,16 @@ def _move_path_to_path_or_stream(src, dst):
         shutil.move(src, dst, copy_function=shutil.copyfile)
 
 
-def _font_to_ps_type3(font_path, chars):
+def _font_to_ps_type3(font_path, glyph_indices):
     """
-    Subset *chars* from the font at *font_path* into a Type 3 font.
+    Subset *glyphs_indices* from the font at *font_path* into a Type 3 font.
 
     Parameters
     ----------
     font_path : path-like
         Path to the font to be subsetted.
-    chars : str
-        The characters to include in the subsetted font.
+    glyph_indices : set[int]
+        The glyphs to include in the subsetted font.
 
     Returns
     -------
@@ -106,7 +106,6 @@ def _font_to_ps_type3(font_path, chars):
         verbatim into a PostScript file.
     """
     font = get_font(font_path, hinting_factor=1)
-    glyph_ids = [font.get_char_index(c) for c in chars]
 
     preamble = """\
 %!PS-Adobe-3.0 Resource-Font
@@ -123,9 +122,9 @@ def _font_to_ps_type3(font_path, chars):
 """.format(font_name=font.postscript_name,
            inv_units_per_em=1 / font.units_per_EM,
            bbox=" ".join(map(str, font.bbox)),
-           encoding=" ".join(f"/{font.get_glyph_name(glyph_id)}"
-                             for glyph_id in glyph_ids),
-           num_glyphs=len(glyph_ids) + 1)
+           encoding=" ".join(f"/{font.get_glyph_name(glyph_index)}"
+                             for glyph_index in glyph_indices),
+           num_glyphs=len(glyph_indices) + 1)
     postamble = """
 end readonly def
 
@@ -146,12 +145,12 @@ def _font_to_ps_type3(font_path, chars):
 """
 
     entries = []
-    for glyph_id in glyph_ids:
-        g = font.load_glyph(glyph_id, LoadFlags.NO_SCALE)
+    for glyph_index in glyph_indices:
+        g = font.load_glyph(glyph_index, LoadFlags.NO_SCALE)
         v, c = font.get_path()
         entries.append(
             "/%(name)s{%(bbox)s sc\n" % {
-                "name": font.get_glyph_name(glyph_id),
+                "name": font.get_glyph_name(glyph_index),
                 "bbox": " ".join(map(str, [g.horiAdvance, 0, *g.bbox])),
             }
             + _path.convert_to_string(
@@ -169,21 +168,20 @@ def _font_to_ps_type3(font_path, chars):
     return preamble + "\n".join(entries) + postamble
 
 
-def _font_to_ps_type42(font_path, chars, fh):
+def _font_to_ps_type42(font_path, glyph_indices, fh):
     """
-    Subset *chars* from the font at *font_path* into a Type 42 font at *fh*.
+    Subset *glyph_indices* from the font at *font_path* into a Type 42 font at *fh*.
 
     Parameters
     ----------
     font_path : path-like
         Path to the font to be subsetted.
-    chars : str
-        The characters to include in the subsetted font.
+    glyph_indices : set[int]
+        The glyphs to include in the subsetted font.
     fh : file-like
         Where to write the font.
     """
-    subset_str = ''.join(chr(c) for c in chars)
-    _log.debug("SUBSET %s characters: %s", font_path, subset_str)
+    _log.debug("SUBSET %s characters: %s", font_path, glyph_indices)
     try:
         kw = {}
         # fix this once we support loading more fonts from a collection
@@ -191,7 +189,7 @@ def _font_to_ps_type42(font_path, chars, fh):
         if font_path.endswith('.ttc'):
             kw['fontNumber'] = 0
         with (fontTools.ttLib.TTFont(font_path, **kw) as font,
-              _backend_pdf_ps.get_glyphs_subset(font_path, subset_str) as subset):
+              _backend_pdf_ps.get_glyphs_subset(font_path, glyph_indices) as subset):
             fontdata = _backend_pdf_ps.font_as_file(subset).getvalue()
             _log.debug(
                 "SUBSET %s %d -> %d", font_path, os.stat(font_path).st_size,
@@ -775,8 +773,7 @@ def draw_text(self, gc, x, y, s, prop, angle, ismath=False, mtext=None):
 
         if mpl.rcParams['ps.useafm']:
             font = self._get_font_afm(prop)
-            ps_name = (font.postscript_name.encode("ascii", "replace")
-                        .decode("ascii"))
+            ps_name = font.postscript_name.encode("ascii", "replace").decode("ascii")
             scale = 0.001 * prop.get_size_in_points()
             thisx = 0
             last_name = ''  # kerns returns 0 for ''.
@@ -799,7 +796,7 @@ def draw_text(self, gc, x, y, s, prop, angle, ismath=False, mtext=None):
             for item in _text_helpers.layout(s, font):
                 ps_name = (item.ft_object.postscript_name
                            .encode("ascii", "replace").decode("ascii"))
-                glyph_name = item.ft_object.get_glyph_name(item.glyph_idx)
+                glyph_name = item.ft_object.get_glyph_name(item.glyph_index)
                 stream.append((ps_name, item.x, glyph_name))
         self.set_color(*gc.get_rgb())
 
@@ -828,13 +825,13 @@ def draw_mathtext(self, gc, x, y, s, prop, angle):
             f"{x:g} {y:g} translate\n"
             f"{angle:g} rotate\n")
         lastfont = None
-        for font, fontsize, num, ox, oy in glyphs:
-            self._character_tracker.track_glyph(font, num)
+        for font, fontsize, glyph_index, ox, oy in glyphs:
+            self._character_tracker.track_glyph(font, glyph_index)
             if (font.postscript_name, fontsize) != lastfont:
                 lastfont = font.postscript_name, fontsize
                 self._pswriter.write(
                     f"/{font.postscript_name} {fontsize} selectfont\n")
-            glyph_name = font.get_glyph_name(font.get_char_index(num))
+            glyph_name = font.get_glyph_name(glyph_index)
             self._pswriter.write(
                 f"{ox:g} {oy:g} moveto\n"
                 f"/{glyph_name} glyphshow\n")
@@ -1072,19 +1069,18 @@ def print_figure_impl(fh):
             print("mpldict begin", file=fh)
             print("\n".join(_psDefs), file=fh)
             if not mpl.rcParams['ps.useafm']:
-                for font_path, chars \
-                        in ps_renderer._character_tracker.used.items():
-                    if not chars:
+                for font_path, glyphs in ps_renderer._character_tracker.used.items():
+                    if not glyphs:
                         continue
                     fonttype = mpl.rcParams['ps.fonttype']
                     # Can't use more than 255 chars from a single Type 3 font.
-                    if len(chars) > 255:
+                    if len(glyphs) > 255:
                         fonttype = 42
                     fh.flush()
                     if fonttype == 3:
-                        fh.write(_font_to_ps_type3(font_path, chars))
+                        fh.write(_font_to_ps_type3(font_path, glyphs))
                     else:  # Type 42 only.
-                        _font_to_ps_type42(font_path, chars, fh)
+                        _font_to_ps_type42(font_path, glyphs, fh)
             print("end", file=fh)
             print("%%EndProlog", file=fh)
 
diff --git a/lib/matplotlib/backends/backend_svg.py b/lib/matplotlib/backends/backend_svg.py
index 0cb6430ec823..d85ba4893958 100644
--- a/lib/matplotlib/backends/backend_svg.py
+++ b/lib/matplotlib/backends/backend_svg.py
@@ -1023,19 +1023,19 @@ def _update_glyph_map_defs(self, glyph_map_new):
         writer = self.writer
         if glyph_map_new:
             writer.start('defs')
-            for char_id, (vertices, codes) in glyph_map_new.items():
-                char_id = self._adjust_char_id(char_id)
+            for glyph_id, (vertices, codes) in glyph_map_new.items():
+                glyph_id = self._adjust_glyph_id(glyph_id)
                 # x64 to go back to FreeType's internal (integral) units.
                 path_data = self._convert_path(
                     Path(vertices * 64, codes), simplify=False)
                 writer.element(
-                    'path', id=char_id, d=path_data,
+                    'path', id=glyph_id, d=path_data,
                     transform=_generate_transform([('scale', (1 / 64,))]))
             writer.end('defs')
             self._glyph_map.update(glyph_map_new)
 
-    def _adjust_char_id(self, char_id):
-        return char_id.replace("%20", "_")
+    def _adjust_glyph_id(self, glyph_id):
+        return glyph_id.replace("%20", "_")
 
     def _draw_text_as_path(self, gc, x, y, s, prop, angle, ismath, mtext=None):
         # docstring inherited
@@ -1067,9 +1067,8 @@ def _draw_text_as_path(self, gc, x, y, s, prop, angle, ismath, mtext=None):
 
         if not ismath:
             font = text2path._get_font(prop)
-            _glyphs = text2path.get_glyphs_with_font(
+            glyph_info, glyph_map_new, rects = text2path.get_glyphs_with_font(
                 font, s, glyph_map=glyph_map, return_new_glyphs_only=True)
-            glyph_info, glyph_map_new, rects = _glyphs
             self._update_glyph_map_defs(glyph_map_new)
 
             for glyph_id, xposition, yposition, scale in glyph_info:
@@ -1091,15 +1090,15 @@ def _draw_text_as_path(self, gc, x, y, s, prop, angle, ismath, mtext=None):
             glyph_info, glyph_map_new, rects = _glyphs
             self._update_glyph_map_defs(glyph_map_new)
 
-            for char_id, xposition, yposition, scale in glyph_info:
-                char_id = self._adjust_char_id(char_id)
+            for glyph_id, xposition, yposition, scale in glyph_info:
+                glyph_id = self._adjust_glyph_id(glyph_id)
                 writer.element(
                     'use',
                     transform=_generate_transform([
                         ('translate', (xposition, yposition)),
                         ('scale', (scale,)),
                         ]),
-                    attrib={'xlink:href': f'#{char_id}'})
+                    attrib={'xlink:href': f'#{glyph_id}'})
 
             for verts, codes in rects:
                 path = Path(verts, codes)
@@ -1223,7 +1222,12 @@ def _get_all_quoted_names(prop):
 
             # Sort the characters by font, and output one tspan for each.
             spans = {}
-            for font, fontsize, thetext, new_x, new_y in glyphs:
+            font_charmaps = {}
+            for font, fontsize, glyph_index, new_x, new_y in glyphs:
+                if font not in font_charmaps:
+                    font_charmaps[font] = {
+                        gind: ccode for ccode, gind in font.get_charmap().items()}
+                ccode = font_charmaps[font].get(glyph_index)
                 entry = fm.ttfFontProperty(font)
                 font_style = {}
                 # Separate font style in its separate attributes
@@ -1238,9 +1242,9 @@ def _get_all_quoted_names(prop):
                 if entry.stretch != 'normal':
                     font_style['font-stretch'] = entry.stretch
                 style = _generate_css({**font_style, **color_style})
-                if thetext == 32:
-                    thetext = 0xa0  # non-breaking space
-                spans.setdefault(style, []).append((new_x, -new_y, thetext))
+                if ccode == 32:
+                    ccode = 0xa0  # non-breaking space
+                spans.setdefault(style, []).append((new_x, -new_y, ccode))
 
             for style, chars in spans.items():
                 chars.sort()  # Sort by increasing x position
diff --git a/lib/matplotlib/dviread.pyi b/lib/matplotlib/dviread.pyi
index 82c0238d39d1..6ddc463295a9 100644
--- a/lib/matplotlib/dviread.pyi
+++ b/lib/matplotlib/dviread.pyi
@@ -8,6 +8,9 @@ from collections.abc import Generator
 from typing import NamedTuple
 from typing import Self
 
+from .ft2font import GlyphIndexType
+
+
 class _dvistate(Enum):
     pre = ...
     outer = ...
@@ -41,9 +44,9 @@ class Text(NamedTuple):
     @property
     def font_effects(self) -> dict[str, float]: ...
     @property
-    def index(self) -> int: ...  # type: ignore[override]
+    def index(self) -> GlyphIndexType: ...  # type: ignore[override]
     @property
-    def glyph_name_or_index(self) -> int | str: ...
+    def glyph_name_or_index(self) -> GlyphIndexType | str: ...
 
 class Dvi:
     file: io.BufferedReader
diff --git a/lib/matplotlib/ft2font.pyi b/lib/matplotlib/ft2font.pyi
index a413cd3c1a76..de04dcd9aadd 100644
--- a/lib/matplotlib/ft2font.pyi
+++ b/lib/matplotlib/ft2font.pyi
@@ -1,6 +1,6 @@
 from enum import Enum, Flag
 import sys
-from typing import BinaryIO, Literal, TypedDict, final, overload, cast
+from typing import BinaryIO, Literal, NewType, TypeAlias, TypedDict, cast, final, overload
 from typing_extensions import Buffer  # < Py 3.12
 
 import numpy as np
@@ -9,6 +9,12 @@ from numpy.typing import NDArray
 __freetype_build_type__: str
 __freetype_version__: str
 
+# We can't change the type hints for standard library chr/ord, so character codes are a
+# simple type alias.
+CharacterCodeType: TypeAlias = int
+# But glyph indices are internal, so use a distinct type hint.
+GlyphIndexType = NewType('GlyphIndexType', int)
+
 class FaceFlags(Flag):
     SCALABLE = cast(int, ...)
     FIXED_SIZES = cast(int, ...)
@@ -202,13 +208,13 @@ class FT2Font(Buffer):
     ) -> None: ...
     def draw_glyphs_to_bitmap(self, antialiased: bool = ...) -> None: ...
     def get_bitmap_offset(self) -> tuple[int, int]: ...
-    def get_char_index(self, codepoint: int) -> int: ...
-    def get_charmap(self) -> dict[int, int]: ...
+    def get_char_index(self, codepoint: CharacterCodeType) -> GlyphIndexType: ...
+    def get_charmap(self) -> dict[CharacterCodeType, GlyphIndexType]: ...
     def get_descent(self) -> int: ...
-    def get_glyph_name(self, index: int) -> str: ...
+    def get_glyph_name(self, index: GlyphIndexType) -> str: ...
     def get_image(self) -> NDArray[np.uint8]: ...
-    def get_kerning(self, left: int, right: int, mode: Kerning) -> int: ...
-    def get_name_index(self, name: str) -> int: ...
+    def get_kerning(self, left: GlyphIndexType, right: GlyphIndexType, mode: Kerning) -> int: ...
+    def get_name_index(self, name: str) -> GlyphIndexType: ...
     def get_num_glyphs(self) -> int: ...
     def get_path(self) -> tuple[NDArray[np.float64], NDArray[np.int8]]: ...
     def get_ps_font_info(
@@ -230,8 +236,8 @@ class FT2Font(Buffer):
     @overload
     def get_sfnt_table(self, name: Literal["pclt"]) -> _SfntPcltDict | None: ...
     def get_width_height(self) -> tuple[int, int]: ...
-    def load_char(self, charcode: int, flags: LoadFlags = ...) -> Glyph: ...
-    def load_glyph(self, glyphindex: int, flags: LoadFlags = ...) -> Glyph: ...
+    def load_char(self, charcode: CharacterCodeType, flags: LoadFlags = ...) -> Glyph: ...
+    def load_glyph(self, glyphindex: GlyphIndexType, flags: LoadFlags = ...) -> Glyph: ...
     def select_charmap(self, i: int) -> None: ...
     def set_charmap(self, i: int) -> None: ...
     def set_size(self, ptsize: float, dpi: float) -> None: ...
diff --git a/lib/matplotlib/tests/baseline_images/test_mathtext/mathtext_cm_21.svg b/lib/matplotlib/tests/baseline_images/test_mathtext/mathtext_cm_21.svg
index 6967f80a1186..cd1fb82317ce 100644
--- a/lib/matplotlib/tests/baseline_images/test_mathtext/mathtext_cm_21.svg
+++ b/lib/matplotlib/tests/baseline_images/test_mathtext/mathtext_cm_21.svg
@@ -1,12 +1,23 @@
 <?xml version="1.0" encoding="utf-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
   "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Created with matplotlib (http://matplotlib.org/) -->
-<svg height="54pt" version="1.1" viewBox="0 0 378 54" width="378pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<svg xmlns:xlink="http://www.w3.org/1999/xlink" width="378pt" height="54pt" viewBox="0 0 378 54" xmlns="http://www.w3.org/2000/svg" version="1.1">
+ <metadata>
+  <rdf:RDF xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:cc="http://creativecommons.org/ns#" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
+   <cc:Work>
+    <dc:type rdf:resource="http://purl.org/dc/dcmitype/StillImage"/>
+    <dc:date>2025-06-05T23:38:03.134386</dc:date>
+    <dc:format>image/svg+xml</dc:format>
+    <dc:creator>
+     <cc:Agent>
+      <dc:title>Matplotlib v3.11.0.dev907+g64fb606e35.d20250606, https://matplotlib.org/</dc:title>
+     </cc:Agent>
+    </dc:creator>
+   </cc:Work>
+  </rdf:RDF>
+ </metadata>
  <defs>
-  <style type="text/css">
-*{stroke-linecap:butt;stroke-linejoin:round;}
-  </style>
+  <style type="text/css">*{stroke-linejoin: round; stroke-linecap: butt}</style>
  </defs>
  <g id="figure_1">
   <g id="patch_1">
@@ -15,721 +26,752 @@ L 378 54
 L 378 0 
 L 0 0 
 z
-" style="fill:#ffffff;"/>
+" style="fill: #ffffff"/>
   </g>
   <g id="text_1">
    <!-- Foo: $\alpha_{i+1}^j = {\rm sin}(2\pi f_j t_i) e^{-5 t_i/\tau}$ -->
-   <defs>
-    <path d="M 4.984375 0 
-L 4.984375 2.6875 
-Q 4.984375 2.9375 5.171875 3.21875 
-L 20.703125 20.40625 
-Q 24.21875 24.21875 26.40625 26.796875 
-Q 28.609375 29.390625 30.75 32.765625 
-Q 32.90625 36.140625 34.15625 39.625 
-Q 35.40625 43.109375 35.40625 47.015625 
-Q 35.40625 51.125 33.890625 54.859375 
-Q 32.375 58.59375 29.375 60.84375 
-Q 26.375 63.09375 22.125 63.09375 
-Q 17.78125 63.09375 14.3125 60.46875 
-Q 10.84375 57.859375 9.421875 53.71875 
-Q 9.8125 53.8125 10.5 53.8125 
-Q 12.75 53.8125 14.328125 52.296875 
-Q 15.921875 50.78125 15.921875 48.390625 
-Q 15.921875 46.09375 14.328125 44.5 
-Q 12.75 42.921875 10.5 42.921875 
-Q 8.15625 42.921875 6.5625 44.546875 
-Q 4.984375 46.1875 4.984375 48.390625 
-Q 4.984375 52.15625 6.390625 55.4375 
-Q 7.8125 58.734375 10.46875 61.296875 
-Q 13.140625 63.875 16.484375 65.234375 
-Q 19.828125 66.609375 23.578125 66.609375 
-Q 29.296875 66.609375 34.21875 64.1875 
-Q 39.15625 61.765625 42.03125 57.34375 
-Q 44.921875 52.9375 44.921875 47.015625 
-Q 44.921875 42.671875 43.015625 38.765625 
-Q 41.109375 34.859375 38.125 31.65625 
-Q 35.15625 28.46875 30.515625 24.40625 
-Q 25.875 20.359375 24.421875 19 
-L 13.09375 8.109375 
-L 22.703125 8.109375 
-Q 29.78125 8.109375 34.546875 8.21875 
-Q 39.3125 8.34375 39.59375 8.59375 
-Q 40.765625 9.859375 42 17.828125 
-L 44.921875 17.828125 
-L 42.09375 0 
-z
-" id="Cmr10-32"/>
-    <path d="M 3.328125 -0.296875 
-L 3.328125 16.015625 
-Q 3.328125 16.796875 4.203125 16.796875 
-L 5.421875 16.796875 
-Q 6 16.796875 6.203125 16.015625 
-Q 8.984375 1.515625 19.671875 1.515625 
-Q 24.421875 1.515625 27.609375 3.65625 
-Q 30.8125 5.8125 30.8125 10.296875 
-Q 30.8125 13.53125 28.3125 15.796875 
-Q 25.828125 18.0625 22.40625 18.890625 
-L 15.71875 20.21875 
-Q 12.359375 20.953125 9.59375 22.453125 
-Q 6.84375 23.96875 5.078125 26.484375 
-Q 3.328125 29 3.328125 32.328125 
-Q 3.328125 36.71875 5.640625 39.515625 
-Q 7.953125 42.328125 11.65625 43.578125 
-Q 15.375 44.828125 19.671875 44.828125 
-Q 24.8125 44.828125 28.609375 42.09375 
-L 31.5 44.578125 
-Q 31.5 44.828125 31.984375 44.828125 
-L 32.71875 44.828125 
-Q 33.015625 44.828125 33.25 44.546875 
-Q 33.5 44.28125 33.5 44 
-L 33.5 30.90625 
-Q 33.5 29.984375 32.71875 29.984375 
-L 31.5 29.984375 
-Q 30.609375 29.984375 30.609375 30.90625 
-Q 30.609375 36.140625 27.703125 39.3125 
-Q 24.8125 42.484375 19.578125 42.484375 
-Q 15.09375 42.484375 11.796875 40.8125 
-Q 8.5 39.15625 8.5 35.109375 
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+    <use xlink:href="#DejaVuSans-61" transform="translate(198.474609 0.015625)"/>
+    <use xlink:href="#DejaVuSans-62" transform="translate(259.753906 0.015625)"/>
+    <use xlink:href="#DejaVuSans-6c" transform="translate(323.230469 0.015625)"/>
+    <use xlink:href="#DejaVuSans-65" transform="translate(351.013672 0.015625)"/>
+    <use xlink:href="#DejaVuSans-20" transform="translate(412.537109 0.015625)"/>
+    <use xlink:href="#STIXGeneral-Italic-1d62a" transform="translate(444.324219 0.015625)"/>
+    <use xlink:href="#DejaVuSans-20" transform="translate(466.324203 0.015625)"/>
+    <use xlink:href="#DejaVuSans-69" transform="translate(498.111313 0.015625)"/>
+    <use xlink:href="#DejaVuSans-73" transform="translate(525.894516 0.015625)"/>
+    <use xlink:href="#DejaVuSans-20" transform="translate(577.994125 0.015625)"/>
+    <use xlink:href="#DejaVuSans-67" transform="translate(609.781235 0.015625)"/>
+    <use xlink:href="#DejaVuSans-6f" transform="translate(673.257797 0.015625)"/>
+    <use xlink:href="#DejaVuSans-6f" transform="translate(734.439438 0.015625)"/>
+    <use xlink:href="#DejaVuSans-64" transform="translate(795.621078 0.015625)"/>
    </g>
   </g>
  </g>
diff --git a/lib/matplotlib/tests/test_backend_pdf.py b/lib/matplotlib/tests/test_backend_pdf.py
index f126fb543e78..fdf0ebbfc871 100644
--- a/lib/matplotlib/tests/test_backend_pdf.py
+++ b/lib/matplotlib/tests/test_backend_pdf.py
@@ -361,13 +361,13 @@ def test_glyphs_subset():
     # non-subsetted FT2Font
     nosubfont = FT2Font(fpath)
     nosubfont.set_text(chars)
+    nosubcmap = nosubfont.get_charmap()
 
     # subsetted FT2Font
-    with get_glyphs_subset(fpath, chars) as subset:
+    glyph_ids = {nosubcmap[ord(c)] for c in chars}
+    with get_glyphs_subset(fpath, glyph_ids) as subset:
         subfont = FT2Font(font_as_file(subset))
     subfont.set_text(chars)
-
-    nosubcmap = nosubfont.get_charmap()
     subcmap = subfont.get_charmap()
 
     # all unique chars must be available in subsetted font
diff --git a/lib/matplotlib/tests/test_ft2font.py b/lib/matplotlib/tests/test_ft2font.py
index b39df1f52996..9ef1f107f1d7 100644
--- a/lib/matplotlib/tests/test_ft2font.py
+++ b/lib/matplotlib/tests/test_ft2font.py
@@ -1,6 +1,7 @@
 import itertools
 import io
 from pathlib import Path
+from typing import cast
 
 import numpy as np
 import pytest
@@ -235,7 +236,7 @@ def enc(name):
     assert unic == after
 
     # This is just a random sample from FontForge.
-    glyph_names = {
+    glyph_names = cast(dict[str, ft2font.GlyphIndexType], {
         'non-existent-glyph-name': 0,
         'plusminus': 115,
         'Racute': 278,
@@ -247,7 +248,7 @@ def enc(name):
         'uni2A02': 4464,
         'u1D305': 5410,
         'u1F0A1': 5784,
-    }
+    })
     for name, index in glyph_names.items():
         assert font.get_name_index(name) == index
         if name == 'non-existent-glyph-name':
diff --git a/lib/matplotlib/textpath.py b/lib/matplotlib/textpath.py
index b57597ded363..02e4cdf27b80 100644
--- a/lib/matplotlib/textpath.py
+++ b/lib/matplotlib/textpath.py
@@ -39,11 +39,9 @@ def _get_font(self, prop):
     def _get_hinting_flag(self):
         return LoadFlags.NO_HINTING
 
-    def _get_char_id(self, font, ccode):
-        """
-        Return a unique id for the given font and character-code set.
-        """
-        return urllib.parse.quote(f"{font.postscript_name}-{ccode:x}")
+    def _get_glyph_id(self, font, glyph):
+        """Return a unique id for the given font and glyph index."""
+        return urllib.parse.quote(f"{font.postscript_name}-{glyph:x}")
 
     def get_text_width_height_descent(self, s, prop, ismath):
         fontsize = prop.get_size_in_points()
@@ -146,11 +144,11 @@ def get_glyphs_with_font(self, font, s, glyph_map=None,
         xpositions = []
         glyph_ids = []
         for item in _text_helpers.layout(s, font):
-            char_id = self._get_char_id(item.ft_object, ord(item.char))
-            glyph_ids.append(char_id)
+            glyph_id = self._get_glyph_id(item.ft_object, item.glyph_index)
+            glyph_ids.append(glyph_id)
             xpositions.append(item.x)
-            if char_id not in glyph_map:
-                glyph_map_new[char_id] = item.ft_object.get_path()
+            if glyph_id not in glyph_map:
+                glyph_map_new[glyph_id] = item.ft_object.get_path()
 
         ypositions = [0] * len(xpositions)
         sizes = [1.] * len(xpositions)
@@ -185,17 +183,17 @@ def get_glyphs_mathtext(self, prop, s, glyph_map=None,
         glyph_ids = []
         sizes = []
 
-        for font, fontsize, ccode, ox, oy in glyphs:
-            char_id = self._get_char_id(font, ccode)
-            if char_id not in glyph_map:
+        for font, fontsize, glyph_index, ox, oy in glyphs:
+            glyph_id = self._get_glyph_id(font, glyph_index)
+            if glyph_id not in glyph_map:
                 font.clear()
                 font.set_size(self.FONT_SCALE, self.DPI)
-                font.load_char(ccode, flags=LoadFlags.NO_HINTING)
-                glyph_map_new[char_id] = font.get_path()
+                font.load_glyph(glyph_index, flags=LoadFlags.NO_HINTING)
+                glyph_map_new[glyph_id] = font.get_path()
 
             xpositions.append(ox)
             ypositions.append(oy)
-            glyph_ids.append(char_id)
+            glyph_ids.append(glyph_id)
             size = fontsize / self.FONT_SCALE
             sizes.append(size)
 
@@ -232,17 +230,16 @@ def get_glyphs_tex(self, prop, s, glyph_map=None,
 
         # Gather font information and do some setup for combining
         # characters into strings.
-        t1_encodings = {}
         for text in page.text:
             font = get_font(text.font_path)
-            char_id = self._get_char_id(font, text.glyph)
-            if char_id not in glyph_map:
+            glyph_id = self._get_glyph_id(font, text.index)
+            if glyph_id not in glyph_map:
                 font.clear()
                 font.set_size(self.FONT_SCALE, self.DPI)
                 font.load_glyph(text.index, flags=LoadFlags.TARGET_LIGHT)
-                glyph_map_new[char_id] = font.get_path()
+                glyph_map_new[glyph_id] = font.get_path()
 
-            glyph_ids.append(char_id)
+            glyph_ids.append(glyph_id)
             xpositions.append(text.x)
             ypositions.append(text.y)
             sizes.append(text.font_size / self.FONT_SCALE)
diff --git a/src/ft2font_wrapper.cpp b/src/ft2font_wrapper.cpp
index cb816efff9a9..f4f9dd6fe009 100644
--- a/src/ft2font_wrapper.cpp
+++ b/src/ft2font_wrapper.cpp
@@ -1772,5 +1772,8 @@ PYBIND11_MODULE(ft2font, m, py::mod_gil_not_used())
 
     m.attr("__freetype_version__") = version_string;
     m.attr("__freetype_build_type__") = FREETYPE_BUILD_TYPE;
+    auto py_int = py::module_::import("builtins").attr("int");
+    m.attr("CharacterCodeType") = py_int;
+    m.attr("GlyphIndexType") = py_int;
     m.def("__getattr__", ft2font__getattr__);
 }