diff --git a/sphinx/_templates/local_md_files.html b/sphinx/_templates/local_md_files.html
index 3a6441e5..c58e1984 100644
--- a/sphinx/_templates/local_md_files.html
+++ b/sphinx/_templates/local_md_files.html
@@ -1,10 +1,25 @@
-{% if local_md_files %}
-<div class="local-md-files">
-  <h3>Local Markdown Files</h3>
-  <ul>
-  {% for item in local_md_files %}
-    <li><a href="{{ pathto(item.link) }}">{{ item.name }}</a></li>
+{% if local_md_headings %}
+<div class="local-md-headings">
+  <h3>Page Headings</h3>
+  {% set ns = namespace(current_level=0) %}
+  {% for item in local_md_headings %}
+    {# If the current heading level is greater than the previous, open new <ul> tags #}
+    {% if item.level > ns.current_level %}
+      {% for i in range(ns.current_level, item.level) %}
+        <ul>
+      {% endfor %}
+    {# If the current heading level is less than the previous, close the open <ul> tags #}
+    {% elif item.level < ns.current_level %}
+      {% for i in range(item.level, ns.current_level) %}
+        </ul>
+      {% endfor %}
+    {% endif %}
+    <li><a href="{{ pathto(item.link) }}">{{ item.text }}</a></li>
+    {% set ns.current_level = item.level %}
+  {% endfor %}
+  {# Close any remaining open <ul> tags #}
+  {% for i in range(ns.current_level) %}
+    </ul>
   {% endfor %}
-  </ul>
 </div>
 {% endif %}
diff --git a/sphinx/local_md_files.py b/sphinx/local_md_files.py
index 8a5963c3..8d513d04 100644
--- a/sphinx/local_md_files.py
+++ b/sphinx/local_md_files.py
@@ -1,30 +1,79 @@
 import os
+import re
 from sphinx.util import logging
 
 logger = logging.getLogger(__name__)
 
-def add_local_md_files(app, pagename, templatename, context, doctree):
+# Set the maximum heading level to include (e.g., include headings up to H3)
+MAX_HEADING_LEVEL = 3
+
+def extract_headings_from_file(filepath, max_level=MAX_HEADING_LEVEL):
+    """
+    Extract Markdown headings (up to max_level) from the file at filepath.
+    Skips fenced code blocks.
+    """
+    headings = []
+    try:
+        with open(filepath, 'r', encoding='utf-8') as f:
+            in_code_block = False
+            for line in f:
+                # Toggle fenced code block state if a line starts with ```
+                if line.strip().startswith("```"):
+                    in_code_block = not in_code_block
+                    continue
+                if in_code_block:
+                    continue
+                # Match Markdown headings: one or more '#' followed by a space and the title.
+                match = re.match(r'^(#{1,})\s+(.*)$', line)
+                if match:
+                    level = len(match.group(1))
+                    if level <= max_level:
+                        heading_text = match.group(2).strip()
+                        # Create a simple slug for the anchor by:
+                        # - converting to lowercase
+                        # - replacing spaces with hyphens
+                        # - removing non-alphanumeric characters (except hyphens)
+                        anchor = re.sub(r'\s+', '-', heading_text.lower())
+                        anchor = re.sub(r'[^a-z0-9\-]', '', anchor)
+                        headings.append({'level': level, 'text': heading_text, 'anchor': anchor})
+    except Exception as e:
+        logger.warning(f"Error reading {filepath}: {e}")
+    return headings
+
+def add_local_md_headings(app, pagename, templatename, context, doctree):
+    """
+    For every Markdown file in the same directory as the current page,
+    extract its headings and add them to the context.
+    """
     srcdir = app.srcdir
     # Determine the directory of the current page (e.g., "directory/file" → "directory")
     directory = os.path.dirname(pagename)
     abs_dir = os.path.join(srcdir, directory)
     if not os.path.isdir(abs_dir):
         logger.warning(f"Directory {abs_dir} not found for page {pagename}.")
-        context['local_md_files'] = []
+        context['local_md_headings'] = []
         return
 
-    md_files = []
+    local_md_headings = []
     for file in os.listdir(abs_dir):
         if file.endswith('.md'):
-            # Optionally: Skip the current file in the list
-            if file == os.path.basename(pagename):
-                continue
-            # Create a link relative to the source directory
-            link = os.path.join(directory, file) if directory else file
-            md_files.append({'name': file, 'link': link})
-    context['local_md_files'] = md_files
+            # Optionally, you may choose to skip the current file:
+            # if file == os.path.basename(pagename):
+            #     continue
+            filepath = os.path.join(abs_dir, file)
+            headings = extract_headings_from_file(filepath)
+            for heading in headings:
+                # Build a full link: if there is a directory, include it in the path.
+                file_link = os.path.join(directory, file) if directory else file
+                full_link = file_link + '#' + heading['anchor']
+                local_md_headings.append({
+                    'level': heading['level'],
+                    'text': heading['text'],
+                    'link': full_link
+                })
+    context['local_md_headings'] = local_md_headings
 
 def setup(app):
-    # Connect the handler to the "html-page-context" event
-    app.connect('html-page-context', add_local_md_files)
+    # Connect our handler to the "html-page-context" event.
+    app.connect('html-page-context', add_local_md_headings)
     return {'version': '0.1', 'parallel_read_safe': True}