diff --git a/python/build/autotools.py b/python/build/autotools.py
index 46fbd273b..d121bf6bf 100644
--- a/python/build/autotools.py
+++ b/python/build/autotools.py
@@ -1,15 +1,17 @@
 import os.path, subprocess, sys
+from typing import Collection, Iterable, Optional
 
 from build.makeproject import MakeProject
 
 class AutotoolsProject(MakeProject):
-    def __init__(self, url, md5, installed, configure_args=[],
-                 autogen=False,
-                 autoreconf=False,
-                 cppflags='',
-                 ldflags='',
-                 libs='',
-                 subdirs=None,
+    def __init__(self, url: str, md5: str, installed: str,
+                 configure_args: Iterable[str]=[],
+                 autogen: bool=False,
+                 autoreconf: bool=False,
+                 cppflags: str='',
+                 ldflags: str='',
+                 libs: str='',
+                 subdirs: Optional[Collection[str]]=None,
                  **kwargs):
         MakeProject.__init__(self, url, md5, installed, **kwargs)
         self.configure_args = configure_args
@@ -20,7 +22,7 @@ class AutotoolsProject(MakeProject):
         self.libs = libs
         self.subdirs = subdirs
 
-    def configure(self, toolchain):
+    def configure(self, toolchain) -> str:
         src = self.unpack(toolchain)
         if self.autogen:
             if sys.platform == 'darwin':
@@ -68,7 +70,7 @@ class AutotoolsProject(MakeProject):
 
         return build
 
-    def _build(self, toolchain):
+    def _build(self, toolchain) -> None:
         build = self.configure(toolchain)
         if self.subdirs is not None:
             for subdir in self.subdirs:
diff --git a/python/build/cmake.py b/python/build/cmake.py
index b41d14698..def58c65d 100644
--- a/python/build/cmake.py
+++ b/python/build/cmake.py
@@ -1,17 +1,19 @@
 import os
 import re
 import subprocess
+from typing import Optional, TextIO
+from collections.abc import Mapping
 
 from build.project import Project
 
-def __write_cmake_compiler(f, language, compiler):
+def __write_cmake_compiler(f: TextIO, language: str, compiler: str) -> None:
     s = compiler.split(' ', 1)
     if len(s) == 2:
         print(f'set(CMAKE_{language}_COMPILER_LAUNCHER {s[0]})', file=f)
         compiler = s[1]
     print(f'set(CMAKE_{language}_COMPILER {compiler})', file=f)
 
-def __write_cmake_toolchain_file(f, toolchain):
+def __write_cmake_toolchain_file(f: TextIO, toolchain) -> None:
     if '-darwin' in toolchain.actual_arch:
         cmake_system_name = 'Darwin'
     elif toolchain.is_windows:
@@ -52,7 +54,7 @@ set(CMAKE_FIND_ROOT_PATH_MODE_LIBRARY ONLY)
 set(CMAKE_FIND_ROOT_PATH_MODE_INCLUDE ONLY)
 """)
 
-def configure(toolchain, src, build, args=(), env=None):
+def configure(toolchain, src: str, build: str, args: list[str]=[], env: Optional[Mapping[str, str]]=None) -> None:
     cross_args = []
 
     if toolchain.is_windows:
@@ -91,16 +93,17 @@ def configure(toolchain, src, build, args=(), env=None):
     subprocess.check_call(configure, env=env, cwd=build)
 
 class CmakeProject(Project):
-    def __init__(self, url, md5, installed, configure_args=[],
-                 windows_configure_args=[],
-                 env=None,
+    def __init__(self, url: str, md5: str, installed: str,
+                 configure_args: list[str]=[],
+                 windows_configure_args: list[str]=[],
+                 env: Optional[Mapping[str, str]]=None,
                  **kwargs):
         Project.__init__(self, url, md5, installed, **kwargs)
         self.configure_args = configure_args
         self.windows_configure_args = windows_configure_args
         self.env = env
 
-    def configure(self, toolchain):
+    def configure(self, toolchain) -> str:
         src = self.unpack(toolchain)
         build = self.make_build_path(toolchain)
         configure_args = self.configure_args
@@ -109,7 +112,7 @@ class CmakeProject(Project):
         configure(toolchain, src, build, configure_args, self.env)
         return build
 
-    def _build(self, toolchain):
+    def _build(self, toolchain) -> None:
         build = self.configure(toolchain)
         subprocess.check_call(['ninja', '-v', 'install'],
                               cwd=build, env=toolchain.env)
diff --git a/python/build/makeproject.py b/python/build/makeproject.py
index 9d498cfbd..c9a2b6eb9 100644
--- a/python/build/makeproject.py
+++ b/python/build/makeproject.py
@@ -1,15 +1,16 @@
 import subprocess, multiprocessing
+from typing import Optional
 
 from build.project import Project
 
 class MakeProject(Project):
-    def __init__(self, url, md5, installed,
-                 install_target='install',
+    def __init__(self, url: str, md5: str, installed: str,
+                 install_target: str='install',
                  **kwargs):
         Project.__init__(self, url, md5, installed, **kwargs)
         self.install_target = install_target
 
-    def get_simultaneous_jobs(self):
+    def get_simultaneous_jobs(self) -> int:
         try:
             # use twice as many simultaneous jobs as we have CPU cores
             return multiprocessing.cpu_count() * 2
@@ -17,17 +18,17 @@ class MakeProject(Project):
             # default to 12, if multiprocessing.cpu_count() is not implemented
             return 12
 
-    def get_make_args(self, toolchain):
+    def get_make_args(self, toolchain) -> list[str]:
         return ['--quiet', '-j' + str(self.get_simultaneous_jobs())]
 
-    def get_make_install_args(self, toolchain):
+    def get_make_install_args(self, toolchain) -> list[str]:
         return ['--quiet', self.install_target]
 
-    def make(self, toolchain, wd, args):
+    def make(self, toolchain, wd: str, args: list[str]) -> None:
         subprocess.check_call(['make'] + args,
                               cwd=wd, env=toolchain.env)
 
-    def build_make(self, toolchain, wd, install=True):
+    def build_make(self, toolchain, wd: str, install: bool=True) -> None:
         self.make(toolchain, wd, self.get_make_args(toolchain))
         if install:
             self.make(toolchain, wd, self.get_make_install_args(toolchain))
diff --git a/python/build/meson.py b/python/build/meson.py
index 084e36610..e585800f1 100644
--- a/python/build/meson.py
+++ b/python/build/meson.py
@@ -1,10 +1,11 @@
 import os
 import subprocess
 import platform
+from typing import Optional
 
 from build.project import Project
 
-def make_cross_file(toolchain):
+def make_cross_file(toolchain) -> str:
     if toolchain.is_windows:
         system = 'windows'
         windres = "windres = '%s'" % toolchain.windres
@@ -80,7 +81,7 @@ endian = '{endian}'
 """)
     return path
 
-def configure(toolchain, src, build, args=()):
+def configure(toolchain, src: str, build: str, args: list[str]=[]) -> None:
     cross_file = make_cross_file(toolchain)
     configure = [
         'meson', 'setup',
@@ -103,18 +104,19 @@ def configure(toolchain, src, build, args=()):
     subprocess.check_call(configure, env=env)
 
 class MesonProject(Project):
-    def __init__(self, url, md5, installed, configure_args=[],
+    def __init__(self, url: str, md5: str, installed: str,
+                 configure_args: list[str]=[],
                  **kwargs):
         Project.__init__(self, url, md5, installed, **kwargs)
         self.configure_args = configure_args
 
-    def configure(self, toolchain):
+    def configure(self, toolchain) -> str:
         src = self.unpack(toolchain)
         build = self.make_build_path(toolchain)
         configure(toolchain, src, build, self.configure_args)
         return build
 
-    def _build(self, toolchain):
+    def _build(self, toolchain) -> None:
         build = self.configure(toolchain)
         subprocess.check_call(['ninja', '-v', 'install'],
                               cwd=build, env=toolchain.env)
diff --git a/python/build/openssl.py b/python/build/openssl.py
index dd02941b5..053fe97b8 100644
--- a/python/build/openssl.py
+++ b/python/build/openssl.py
@@ -1,13 +1,14 @@
 import subprocess
+from typing import Optional
 
 from build.makeproject import MakeProject
 
 class OpenSSLProject(MakeProject):
-    def __init__(self, url, md5, installed,
+    def __init__(self, url: str, md5: str, installed: str,
                  **kwargs):
         MakeProject.__init__(self, url, md5, installed, install_target='install_dev', **kwargs)
 
-    def get_make_args(self, toolchain):
+    def get_make_args(self, toolchain) -> list[str]:
         return MakeProject.get_make_args(self, toolchain) + [
             'CC=' + toolchain.cc,
             'CFLAGS=' + toolchain.cflags,
@@ -17,13 +18,13 @@ class OpenSSLProject(MakeProject):
             'build_libs',
         ]
 
-    def get_make_install_args(self, toolchain):
+    def get_make_install_args(self, toolchain) -> list[str]:
         # OpenSSL's Makefile runs "ranlib" during installation
         return MakeProject.get_make_install_args(self, toolchain) + [
             'RANLIB=' + toolchain.ranlib,
         ]
 
-    def _build(self, toolchain):
+    def _build(self, toolchain) -> None:
         src = self.unpack(toolchain, out_of_tree=False)
 
         # OpenSSL has a weird target architecture scheme with lots of
diff --git a/python/build/project.py b/python/build/project.py
index bf787cf43..3607d4942 100644
--- a/python/build/project.py
+++ b/python/build/project.py
@@ -1,16 +1,18 @@
 import os, shutil
 import re
+from typing import cast, BinaryIO, Optional
 
 from build.download import download_and_verify
 from build.tar import untar
 from build.quilt import push_all
 
 class Project:
-    def __init__(self, url, md5, installed, name=None, version=None,
-                 base=None,
-                 patches=None,
+    def __init__(self, url: str, md5: str, installed: str,
+                 name: Optional[str]=None, version: Optional[str]=None,
+                 base: Optional[str]=None,
+                 patches: Optional[str]=None,
                  edits=None,
-                 use_cxx=False):
+                 use_cxx: bool=False):
         if base is None:
             basename = os.path.basename(url)
             m = re.match(r'^(.+)\.(tar(\.(gz|bz2|xz|lzma))?|zip)$', basename)
@@ -39,10 +41,10 @@ class Project:
         self.edits = edits
         self.use_cxx = use_cxx
 
-    def download(self, toolchain):
+    def download(self, toolchain) -> str:
         return download_and_verify(self.url, self.md5, toolchain.tarball_path)
 
-    def is_installed(self, toolchain):
+    def is_installed(self, toolchain) -> bool:
         tarball = self.download(toolchain)
         installed = os.path.join(toolchain.install_prefix, self.installed)
         tarball_mtime = os.path.getmtime(tarball)
@@ -51,7 +53,7 @@ class Project:
         except FileNotFoundError:
             return False
 
-    def unpack(self, toolchain, out_of_tree=True):
+    def unpack(self, toolchain, out_of_tree: bool=True) -> str:
         if out_of_tree:
             parent_path = toolchain.src_path
         else:
@@ -72,7 +74,7 @@ class Project:
 
         return path
 
-    def make_build_path(self, toolchain, lazy=False):
+    def make_build_path(self, toolchain, lazy: bool=False) -> str:
         path = os.path.join(toolchain.build_path, self.base)
         if lazy and os.path.isdir(path):
             return path
@@ -83,5 +85,5 @@ class Project:
         os.makedirs(path, exist_ok=True)
         return path
 
-    def build(self, toolchain):
+    def build(self, toolchain) -> None:
         self._build(toolchain)
diff --git a/python/build/quilt.py b/python/build/quilt.py
index 876453d2b..8751404db 100644
--- a/python/build/quilt.py
+++ b/python/build/quilt.py
@@ -1,9 +1,10 @@
 import subprocess
+from typing import Union
 
-def run_quilt(toolchain, cwd, patches_path, *args):
+def run_quilt(toolchain, cwd: str, patches_path: str, *args: str) -> None:
     env = dict(toolchain.env)
     env['QUILT_PATCHES'] = patches_path
     subprocess.check_call(['quilt'] + list(args), cwd=cwd, env=env)
 
-def push_all(toolchain, src_path, patches_path):
+def push_all(toolchain, src_path: str, patches_path: str) -> None:
     run_quilt(toolchain, src_path, patches_path, 'push', '-a')
diff --git a/python/build/verify.py b/python/build/verify.py
index e22ff274d..763f224ce 100644
--- a/python/build/verify.py
+++ b/python/build/verify.py
@@ -1,6 +1,7 @@
 import hashlib
+from typing import cast, Any, BinaryIO
 
-def feed_file(h, f):
+def feed_file(h: Any, f: BinaryIO) -> None:
     """Feed data read from an open file into the hashlib instance."""
 
     while True:
@@ -10,20 +11,20 @@ def feed_file(h, f):
             break
         h.update(data)
 
-def feed_file_path(h, path):
+def feed_file_path(h: Any, path: str) -> None:
     """Feed data read from a file (to be opened by this function) into the hashlib instance."""
 
     with open(path, 'rb') as f:
         feed_file(h, f)
 
-def file_digest(algorithm, path):
+def file_digest(algorithm: Any, path: str) -> str:
     """Calculate the digest of a file and return it in hexadecimal notation."""
 
     h = algorithm()
     feed_file_path(h, path)
-    return h.hexdigest()
+    return cast(str, h.hexdigest())
 
-def guess_digest_algorithm(digest):
+def guess_digest_algorithm(digest: str) -> Any:
     l = len(digest)
     if l == 32:
         return hashlib.md5
@@ -36,7 +37,7 @@ def guess_digest_algorithm(digest):
     else:
         return None
 
-def verify_file_digest(path, expected_digest):
+def verify_file_digest(path: str, expected_digest: str) -> bool:
     """Verify the digest of a file, and return True if the digest matches with the given expected digest."""
 
     algorithm = guess_digest_algorithm(expected_digest)
diff --git a/python/build/zlib.py b/python/build/zlib.py
index c5aeb8c30..98eede580 100644
--- a/python/build/zlib.py
+++ b/python/build/zlib.py
@@ -1,13 +1,14 @@
 import subprocess
+from typing import Optional
 
 from build.makeproject import MakeProject
 
 class ZlibProject(MakeProject):
-    def __init__(self, url, md5, installed,
+    def __init__(self, url: str, md5: str, installed: str,
                  **kwargs):
         MakeProject.__init__(self, url, md5, installed, **kwargs)
 
-    def get_make_args(self, toolchain):
+    def get_make_args(self, toolchain) -> list[str]:
         return MakeProject.get_make_args(self, toolchain) + [
             'CC=' + toolchain.cc + ' ' + toolchain.cppflags + ' ' + toolchain.cflags,
             'CPP=' + toolchain.cc + ' -E ' + toolchain.cppflags,
@@ -18,13 +19,13 @@ class ZlibProject(MakeProject):
             'libz.a'
         ]
 
-    def get_make_install_args(self, toolchain):
+    def get_make_install_args(self, toolchain) -> list[str]:
         return [
             'RANLIB=' + toolchain.ranlib,
             self.install_target
         ]
 
-    def _build(self, toolchain):
+    def _build(self, toolchain) -> None:
         src = self.unpack(toolchain, out_of_tree=False)
 
         subprocess.check_call(['./configure', '--prefix=' + toolchain.install_prefix, '--static'],