diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index fff93d262e3997fca316a9747b08bf78f7b4ebd4..ce53fa814662ee22de440f72f4f14d82b5a41d95 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -18,7 +18,7 @@ jobs:
         -
             uses: actions/setup-python@v1
             with:
-                python-version: '3.x' 
+                python-version: '3.x'
         -   name: "Main Script"
             run: |
                 curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-flake8.sh
@@ -32,19 +32,33 @@ jobs:
         -
             uses: actions/setup-python@v1
             with:
-                python-version: '3.x' 
+                python-version: '3.x'
         -   name: "Main Script"
             run: |
                 EXTRA_INSTALL="pymbolic matplotlib"
                 curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-pylint.sh
                 . ./prepare-and-run-pylint.sh "$(basename $GITHUB_REPOSITORY)" test/test_*.py
 
+    mypy:
+        name: Mypy
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v2
+        -
+            uses: actions/setup-python@v1
+            with:
+                python-version: '3.x'
+        -   name: "Main Script"
+            run: |
+                curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-mypy.sh
+                . ./prepare-and-run-mypy.sh python3 mypy"
+
     pytest:
         name: Pytest on Py${{ matrix.python-version }}
         runs-on: ubuntu-latest
         strategy:
             matrix:
-                python-version: [2.7, 3.6, 3.7, 3.8, pypy2, pypy3]
+                python-version: [3.6, 3.7, 3.8, pypy3]
         steps:
         -   uses: actions/checkout@v2
         -
diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
index 04de81190a88c3ce7f247aace052551281fb9f4d..aae441a228fac6ba22e456ef156d763e536e49ad 100644
--- a/.gitlab-ci.yml
+++ b/.gitlab-ci.yml
@@ -1,17 +1,3 @@
-Python 2.7:
-  script:
-  - py_version=2.7
-  - export EXTRA_INSTALL="numpy"
-  - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
-  - ". ./build-and-test-py-project.sh"
-  tags:
-  - python2.7
-  except:
-  - tags
-  artifacts:
-    reports:
-      junit: test/pytest.xml
-
 Python 3:
   script:
   - py_version=3
@@ -35,6 +21,15 @@ Flake8:
   except:
   - tags
 
+Mypy:
+  script:
+  - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-mypy.sh
+  - ". ./prepare-and-run-mypy.sh python3 mypy"
+  tags:
+  - python3
+  except:
+  - tags
+
 Pylint:
   script:
   - EXTRA_INSTALL="pymbolic matplotlib"
diff --git a/pytools/__init__.py b/pytools/__init__.py
index d3dcb7722808e72c5166e1c3fc45a6e23992c1a1..0567920e03400cc3557c91040d13f882c48df037 100644
--- a/pytools/__init__.py
+++ b/pytools/__init__.py
@@ -26,10 +26,13 @@ THE SOFTWARE.
 """
 
 
+from functools import reduce
 import operator
 import sys
 import logging
-from functools import reduce
+from typing import (
+        Any, Callable, Dict, Iterable, List, Optional, Set, Tuple, TypeVar)
+
 
 import six
 from six.moves import range, zip, intern, input
@@ -152,6 +155,13 @@ Sorting in natural order
 .. autofunction:: natsorted
 """
 
+# {{{ type variables
+
+T = TypeVar("T")
+F = TypeVar('F', bound=Callable[..., Any])
+
+# }}}
+
 
 # {{{ math --------------------------------------------------------------------
 
@@ -236,7 +246,7 @@ class RecordWithoutPickling(object):
     will be individually derived from this class.
     """
 
-    __slots__ = []
+    __slots__: List[str] = []
 
     def __init__(self, valuedict=None, exclude=None, **kwargs):
         assert self.__class__ is not Record
@@ -293,7 +303,7 @@ class RecordWithoutPickling(object):
 
 
 class Record(RecordWithoutPickling):
-    __slots__ = []
+    __slots__: List[str] = []
 
     def __getstate__(self):
         return dict(
@@ -417,7 +427,7 @@ class DependentDictionary(object):
 
 # {{{ assertive accessors
 
-def one(iterable):
+def one(iterable: Iterable[T]) -> T:
     """Return the first entry of *iterable*. Assert that *iterable* has only
     that one entry.
     """
@@ -439,7 +449,10 @@ def one(iterable):
     return v
 
 
-def is_single_valued(iterable, equality_pred=operator.eq):
+def is_single_valued(
+        iterable: Iterable[T],
+        equality_pred: Callable[[T, T], bool] = operator.eq
+        ) -> bool:
     it = iter(iterable)
     try:
         first_item = next(it)
@@ -460,7 +473,10 @@ def all_roughly_equal(iterable, threshold):
             equality_pred=lambda a, b: abs(a-b) < threshold)
 
 
-def single_valued(iterable, equality_pred=operator.eq):
+def single_valued(
+        iterable: Iterable[T],
+        equality_pred: Callable[[T, T], bool] = operator.eq
+        ) -> T:
     """Return the first entry of *iterable*; Assert that other entries
     are the same with the first entry of *iterable*.
     """
@@ -484,7 +500,7 @@ def single_valued(iterable, equality_pred=operator.eq):
 
 # {{{ memoization / attribute storage
 
-def memoize(*args, **kwargs):
+def memoize(*args: F, **kwargs: Any) -> F:
     """Stores previously computed function values in a cache.
 
     Two keyword-only arguments are supported:
@@ -498,8 +514,10 @@ def memoize(*args, **kwargs):
 
     use_kw = bool(kwargs.pop('use_kwargs', False))
 
+    default_key_func: Optional[Callable[..., Any]]
+
     if use_kw:
-        def default_key_func(*inner_args, **inner_kwargs):
+        def default_key_func(*inner_args, **inner_kwargs):  # noqa pylint:disable=function-redefined
             return inner_args, frozenset(six.iteritems(inner_kwargs))
     else:
         default_key_func = None
@@ -600,7 +618,7 @@ def memoize_on_first_arg(function, cache_dict_name=None):
     return new_wrapper
 
 
-def memoize_method(method):
+def memoize_method(method: F) -> F:
     """Supports cache deletion via ``method_name.clear_cache(self)``.
 
     .. note::
@@ -1831,7 +1849,8 @@ def generate_unique_names(prefix):
         try_num += 1
 
 
-def generate_numbered_unique_names(prefix, num=None):
+def generate_numbered_unique_names(
+        prefix: str, num: Optional[int] = None) -> Iterable[Tuple[int, str]]:
     if num is None:
         yield (0, prefix)
         num = 0
@@ -1853,18 +1872,20 @@ class UniqueNameGenerator(object):
     .. automethod:: add_names
     .. automethod:: __call__
     """
-    def __init__(self, existing_names=None, forced_prefix=""):
+    def __init__(self,
+            existing_names: Optional[Set[str]] = None,
+            forced_prefix: str = ""):
         if existing_names is None:
             existing_names = set()
 
         self.existing_names = existing_names.copy()
         self.forced_prefix = forced_prefix
-        self.prefix_to_counter = {}
+        self.prefix_to_counter: Dict[str, int] = {}
 
-    def is_name_conflicting(self, name):
+    def is_name_conflicting(self, name: str) -> bool:
         return name in self.existing_names
 
-    def _name_added(self, name):
+    def _name_added(self, name: str) -> None:
         """Callback to alert subclasses when a name has been added.
 
         .. note::
@@ -1874,7 +1895,7 @@ class UniqueNameGenerator(object):
         """
         pass
 
-    def add_name(self, name):
+    def add_name(self, name: str) -> None:
         if self.is_name_conflicting(name):
             raise ValueError("name '%s' conflicts with existing names")
         if not name.startswith(self.forced_prefix):
@@ -1883,11 +1904,11 @@ class UniqueNameGenerator(object):
         self.existing_names.add(name)
         self._name_added(name)
 
-    def add_names(self, names):
+    def add_names(self, names: Iterable[str]) -> None:
         for name in names:
             self.add_name(name)
 
-    def __call__(self, based_on="id"):
+    def __call__(self, based_on: str = "id") -> str:
         based_on = self.forced_prefix + based_on
 
         counter = self.prefix_to_counter.get(based_on, None)
diff --git a/pytools/py.typed b/pytools/py.typed
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/run-mypy.sh b/run-mypy.sh
new file mode 100755
index 0000000000000000000000000000000000000000..43e64854d17710b3e5835c6fe8f2624b9708f162
--- /dev/null
+++ b/run-mypy.sh
@@ -0,0 +1,3 @@
+#! /bin/bash
+
+mypy pytools
diff --git a/setup.cfg b/setup.cfg
index 4f28d744a43e004359603baf770d76abca656fa4..9ce1073847ce374bb30f029a4d97a2ca931df549 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -2,5 +2,18 @@
 ignore = E126,E127,E128,E123,E226,E241,E242,E265,E402,W503,E731
 max-line-length=85
 exclude=pytools/arithmetic_container.py,pytools/decorator.py
+
 [wheel]
 universal = 1
+
+[mypy]
+ignore_missing_imports = True
+
+[mypy-pytools.mpiwrap]
+ignore_errors = True
+
+[mypy-pytools.persistent_dict]
+ignore_errors = True
+
+[mypy-pytools.stopwatch]
+ignore_errors = True
diff --git a/setup.py b/setup.py
index adba753c7690f5c7a258d324d3799a0aa98618ca..145ddd6f34dabc21bb79e3b1b56379f4aef219b5 100644
--- a/setup.py
+++ b/setup.py
@@ -25,9 +25,6 @@ setup(name="pytools",
           'Natural Language :: English',
           'Programming Language :: Python',
           'Programming Language :: Python',
-          'Programming Language :: Python :: 2',
-          'Programming Language :: Python :: 2.6',
-          'Programming Language :: Python :: 2.7',
           'Programming Language :: Python :: 3',
           'Programming Language :: Python :: 3.4',
           'Programming Language :: Python :: 3.5',
@@ -48,6 +45,8 @@ setup(name="pytools",
           "numpy>=1.6.0",
           ],
 
+      package_data={"pytools": ["py.typed"]},
+
       author="Andreas Kloeckner",
       url="http://pypi.python.org/pypi/pytools",
       author_email="inform@tiker.net",