diff --git a/tools/c-parser/INSTALL b/tools/c-parser/INSTALL
index bddfdb97f..6bcf4eb15 100644
--- a/tools/c-parser/INSTALL
+++ b/tools/c-parser/INSTALL
@@ -9,7 +9,7 @@
 # Installation instructions for the C parser
 
 NB: These instructions apply to the stand-alone release of the C parser.
-If this is in an L4.verified checkout, see the top-level README instead.
+If this is in an L4.verified checkout, see the top-level README.md instead.
 
 This code requires Isabelle2018 and the MLton SML compiler.
 
@@ -46,7 +46,7 @@ Run Isabelle with this directory as an argument, e.g.:
     isabelle jedit -d src -l CParser foo.thy
 
 If that worked, then the C parser has been loaded successfully.
-See the README and PDF documentation for further instructions.
+See the README.md file and PDF documentation for further instructions.
 
 ## Other tools
 
diff --git a/tools/c-parser/README b/tools/c-parser/README.md
similarity index 62%
rename from tools/c-parser/README
rename to tools/c-parser/README.md
index 57d448ba9..e5a4a971a 100644
--- a/tools/c-parser/README
+++ b/tools/c-parser/README.md
@@ -1,31 +1,33 @@
-#
-# Copyright 2014, NICTA
-#
-# This software may be distributed and modified according to the terms of
-# the BSD 2-Clause license. Note that NO WARRANTY is provided.
-# See "LICENSE_BSD2.txt" for details.
-#
-# @TAG(NICTA_BSD)
-#
+<!--
+ Copyright 2014, NICTA
 
-This is the NICTA StrictC translation tool.
+ This software may be distributed and modified according to the terms of
+ the BSD 2-Clause license. Note that NO WARRANTY is provided.
+ See "LICENSE_BSD2.txt" for details.
 
-To install, see the file INSTALL in the src/c-parser directory.
+ @TAG(NICTA_BSD)
+-->
+
+The StrictC translation tool
+============================
+
+To install, see the file INSTALL in the `src/c-parser` directory.
 
 To use:
 
 1. Use the heap CParser that is created by installation
 2. Import the theory CTranslation
 3. Load ('install') C files into your theories with the Isar command
-   install_C_file.
+   `install_C_file`.
 
-See docs/ctranslation.pdf for more information about the options
+See `docs/ctranslation.pdf` for more information about the options
 and C language semantics that this tool provides.
 
-See many examples in the testfiles directory.  For example,
-breakcontinue.thy is a fairly involved demonstration of doing things
+See also the examples in the testfiles directory.  For example,
+`breakcontinue.thy` is a fairly involved demonstration of doing things
 the hard way.
 
+
 ----------------------------------------------------------------------
 The translation tool builds on various open source projects by others.
 
@@ -34,7 +36,7 @@ The translation tool builds on various open source projects by others.
    Sources for this are found in the Simpl/ directory.  The
    code is covered by an LGPL licence.
 
-   See http://afp.sourceforge.net/entries/Simpl.shtml
+   See https://isa-afp.org/entries/Simpl.shtml
 
 2. Code from SML/NJ:
    - an implementation of binary sets (Binaryset.ML)
diff --git a/tools/c-parser/mkrelease b/tools/c-parser/mkrelease
index d8bd10c35..09e18b119 100755
--- a/tools/c-parser/mkrelease
+++ b/tools/c-parser/mkrelease
@@ -118,7 +118,7 @@ c-parser
 EOF
 
 echo "Rearranging directories"
-/bin/mv -v "$outputdir/src/tools/c-parser/README" "$outputdir"
+/bin/mv -v "$outputdir/src/tools/c-parser/README.md" "$outputdir"
 /bin/mv -v "$outputdir/src/tools/c-parser" "$outputdir/src/"
 rmdir "$outputdir/src/tools"