diff --git a/.github/workflows/lint.yml b/.github/workflows/lint.yml
index f51d2cc..e3185de 100644
--- a/.github/workflows/lint.yml
+++ b/.github/workflows/lint.yml
@@ -2,6 +2,9 @@ name: Lint
 on:
   pull_request:
 
+permissions:
+  contents: read
+
 jobs:
   flake8:
     runs-on: ubuntu-latest
@@ -9,10 +12,34 @@ jobs:
       - uses: actions/checkout@v3
       - uses: actions/setup-python@v4
         with:
-          python-version: 3.8
+          python-version: 3.9
 
       - uses: TrueBrain/actions-flake8@v2
         with:
           flake8_version: 6.0.0
           max_line_length: 120
-          plugins: flake8-isort==6.0.0 flake8-quotes==3.3.2
+          plugins: flake8-isort==6.1.2 flake8-quotes==3.4.0 flake8-commas==4.0.0
+
+  mypy:
+      runs-on: ubuntu-latest
+
+      steps:
+        - uses: actions/checkout@v4
+        - uses: actions/setup-python@v5
+          with:
+            python-version: 3.9
+
+        - run: |
+            pip install poetry
+            poetry install --with=mypy
+
+        - run: |
+            poetry run mypy \
+              --follow-untyped-imports \
+              --disallow-any-unimported \
+              --disallow-untyped-defs \
+              --check-untyped-defs \
+              --strict-equality \
+              --warn-redundant-casts \
+              --warn-unused-ignores \
+              geo_extensions
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index dcab4fe..a102f04 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -3,12 +3,15 @@ name: Test
 on:
   pull_request:
 
+permissions:
+  contents: read
+
 jobs:
   pytest:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: ['3.8', '3.9', '3.10', '3.11']
+        python-version: ['3.9', '3.10', '3.11', '3.12']
       fail-fast: false
 
     steps:
diff --git a/README.md b/README.md
index 23e6558..bb78401 100644
--- a/README.md
+++ b/README.md
@@ -12,7 +12,7 @@ functions. A transformation function is any function with the following
 signature:
 
 ```python
-def transformation(polygon: Polygon) -> Generator[Polygon, None, None]:
+def transformation(polygon: Polygon) -> Generator[Polygon]:
     ...
 ```
 
diff --git a/geo_extensions/transformations.py b/geo_extensions/transformations.py
index 047ffac..1b0c9a2 100644
--- a/geo_extensions/transformations.py
+++ b/geo_extensions/transformations.py
@@ -38,7 +38,7 @@
 ordered in the shapely flat space.
 """
 
-from typing import List, Tuple
+from typing import cast
 
 import shapely.ops
 from shapely.geometry import LineString, Polygon
@@ -50,8 +50,8 @@
 )
 from geo_extensions.types import Transformation, TransformationResult
 
-Point = Tuple[float, float]
-Bbox = List[Point]
+Point = tuple[float, float]
+Bbox = list[Point]
 
 ANTIMERIDIAN = LineString([(180, 90), (180, -90)])
 
@@ -63,7 +63,9 @@ def simplify_polygon(tolerance: float, preserve_topology: bool = True) -> Transf
     """
     def simplify(polygon: Polygon) -> TransformationResult:
         """Perform a shapely simplify operation on the polygon."""
-        yield polygon.simplify(tolerance, preserve_topology)
+        # NOTE(reweeden): I have been unable to produce a situation where a
+        # polygon is simplified to a geometry other than Polygon.
+        yield cast(Polygon, polygon.simplify(tolerance, preserve_topology))
 
     return simplify
 
@@ -139,7 +141,7 @@ def _shift_polygon(polygon: Polygon) -> Polygon:
 
     return Polygon([
         ((360.0 + lon) % 360, lat)
-        for lon, lat in polygon.boundary.coords
+        for lon, lat in polygon.exterior.coords
     ])
 
 
@@ -149,7 +151,7 @@ def _shift_polygon_back(polygon: Polygon) -> Polygon:
     _, _, max_lon, _ = polygon.bounds
     return Polygon([
         (_adjust_lon(lon, max_lon), lat)
-        for lon, lat in polygon.boundary.coords
+        for lon, lat in polygon.exterior.coords
     ])
 
 
@@ -165,13 +167,13 @@ def _adjust_lon(lon: float, max_lon: float) -> float:
 def _split_polygon(
     polygon: Polygon,
     line: LineString,
-) -> List[Polygon]:
+) -> list[Polygon]:
     split_collection = shapely.ops.split(polygon, line)
 
     return [
-        orient(poly)
-        for poly in split_collection.geoms
-        if not _ignore_polygon(poly)
+        orient(geom)
+        for geom in split_collection.geoms
+        if isinstance(geom, Polygon) and not _ignore_polygon(geom)
     ]
 
 
diff --git a/geo_extensions/transformer.py b/geo_extensions/transformer.py
index befc67d..f9dd713 100644
--- a/geo_extensions/transformer.py
+++ b/geo_extensions/transformer.py
@@ -1,4 +1,4 @@
-from typing import Iterable, List, Sequence, Tuple
+from collections.abc import Iterable, Sequence
 
 from shapely import Geometry, wkt
 from shapely.geometry import MultiPolygon, Polygon, shape
@@ -12,7 +12,7 @@ class Transformer:
     def __init__(self, transformations: Sequence[Transformation]):
         self.transformations = transformations
 
-    def from_geo_json(self, geo_json: dict) -> List[Polygon]:
+    def from_geo_json(self, geo_json: dict) -> list[Polygon]:
         """Load and transform an object from a GeoJSON dict.
 
         :returns: a list of transformed polygons
@@ -24,7 +24,7 @@ def from_geo_json(self, geo_json: dict) -> List[Polygon]:
 
         return self.transform(polygons)
 
-    def from_wkt(self, wkt_str: str) -> List[Polygon]:
+    def from_wkt(self, wkt_str: str) -> list[Polygon]:
         """Load and transform an object from a WKT string.
 
         :returns: a list of transformed polygons
@@ -36,7 +36,7 @@ def from_wkt(self, wkt_str: str) -> List[Polygon]:
 
         return self.transform(polygons)
 
-    def transform(self, polygons: Iterable[Polygon]) -> List[Polygon]:
+    def transform(self, polygons: Iterable[Polygon]) -> list[Polygon]:
         """Perform the transformation chain on a sequence of polygons.
 
         :returns: a list of transformed polygons
@@ -46,7 +46,7 @@ def transform(self, polygons: Iterable[Polygon]) -> List[Polygon]:
             _apply_transformations(
                 polygons,
                 tuple(self.transformations),
-            )
+            ),
         )
 
 
@@ -70,7 +70,7 @@ def to_polygons(obj: Geometry) -> TransformationResult:
 
 def _apply_transformations(
     polygons: Iterable[Polygon],
-    transformations: Tuple[Transformation, ...],
+    transformations: tuple[Transformation, ...],
 ) -> TransformationResult:
     if not transformations:
         yield from polygons
diff --git a/geo_extensions/types.py b/geo_extensions/types.py
index 937c3e0..778cf95 100644
--- a/geo_extensions/types.py
+++ b/geo_extensions/types.py
@@ -1,6 +1,6 @@
-from typing import Callable, Generator
+from collections.abc import Callable, Generator
 
 from shapely.geometry import Polygon
 
-TransformationResult = Generator[Polygon, None, None]
+TransformationResult = Generator[Polygon]
 Transformation = Callable[[Polygon], TransformationResult]
diff --git a/pyproject.toml b/pyproject.toml
index 3c1a774..7e248ed 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -12,12 +12,17 @@ readme = "README.md"
 packages = [{include = "geo_extensions"}]
 
 [tool.poetry.dependencies]
-python = "^3.8"
+python = "^3.9"
+
 shapely = "^2.0.3"
 
 [tool.poetry.group.dev.dependencies]
 pytest = "^8.0.1"
 hypothesis = "^6.98.8"
 
+[tool.poetry.group.mypy.dependencies]
+mypy = "^1.16.1"
+types-shapely = "^2.0.3"
+
 [tool.isort]
 profile = "black"
diff --git a/tests/test_geo_extensions.py b/tests/test_geo_extensions.py
index 4f5542f..7b31b25 100644
--- a/tests/test_geo_extensions.py
+++ b/tests/test_geo_extensions.py
@@ -14,5 +14,5 @@ def test_default_transformer(data_path):
             (-68.93161319601728, 81.16999707795055),
             (-64.74688665108201, 80.78217738556877),
             (-64.18242781701073, 80.92318071697005),
-        ])
+        ]),
     ]
diff --git a/tests/test_transformations.py b/tests/test_transformations.py
index 5c207fb..7df1a51 100644
--- a/tests/test_transformations.py
+++ b/tests/test_transformations.py
@@ -6,11 +6,54 @@
 
 from geo_extensions.transformations import (
     drop_z_coordinate,
+    simplify_polygon,
     split_polygon_on_antimeridian_ccw,
     split_polygon_on_antimeridian_fixed_size,
 )
 
 
+def test_simplify():
+    polygon = Polygon([
+        (20, 0),
+        (20, 0),
+        (20, 10),
+        (0, 10),
+        (0, 0),
+        (20, 0),
+    ])
+    assert list(simplify_polygon(0.01)(polygon)) == [
+        Polygon([
+            (20, 0),
+            (20, 10),
+            (0, 10),
+            (0, 0),
+            (20, 0),
+        ]),
+    ]
+
+
+def test_simplify_line():
+    polygon = Polygon([
+        (20, 0),
+        (20, 10),
+        (20, 10),
+        (20, 0),
+        (20, 0),
+    ])
+    assert list(simplify_polygon(0.01)(polygon)) == [
+        Polygon([
+            (20, 0),
+            (20, 10),
+            (20, 10),
+            (20, 0),
+        ]),
+    ]
+
+    assert list(simplify_polygon(0.01, preserve_topology=False)(polygon)) == [
+        Polygon([]),
+    ]
+
+
 def test_drop_z_coordinate():
     polygon = Polygon([
         (180, 1, 10),
@@ -26,7 +69,7 @@ def test_drop_z_coordinate():
             (-179.999, 0),
             (-179.999, 1),
             (180, 1),
-        ])
+        ]),
     ]
 
 
@@ -53,7 +96,7 @@ def test_split_polygon_on_antimeridian_ccw_returns_ccw(polygon):
     polygon=strategies.rectangles(
         # Very small polygons near the antimeridian will be culled.
         lons=st.floats(min_value=-179.990, max_value=180),
-    )
+    ),
 )
 @settings(suppress_health_check=[HealthCheck.filter_too_much])
 def test_split_polygon_on_antimeridian_ccw_returns_non_empty_list(polygon):
@@ -64,7 +107,7 @@ def test_split_polygon_on_antimeridian_ccw_returns_empty_list():
     # There is a case where the input polygon is really small, and both split
     # parts are culled.
     polygon = Polygon([
-        (180, 1), (180, 0), (-179.999, 0), (-179.999, 1), (180, 1)
+        (180, 1), (180, 0), (-179.999, 0), (-179.999, 1), (180, 1),
     ])
     assert list(split_polygon_on_antimeridian_ccw(polygon)) == []
 
@@ -137,7 +180,7 @@ def test_split_polygon_on_antimeridian_ccw_west():
     """Polygon is mostly west of the IDL"""
     polygon = Polygon([
         (170., 70.), (170., 60.), (-179., 60.),
-        (-179., 70.), (170., 70.)
+        (-179., 70.), (170., 70.),
     ])
     assert not polygon.exterior.is_ccw
     polygons = list(split_polygon_on_antimeridian_ccw(polygon))
@@ -168,7 +211,7 @@ def test_split_polygon_on_antimeridian_ccw_east():
     """Polygon is mostly east of the IDL"""
     polygon = Polygon([
         (179., 70.), (179., 60.), (-170., 60.),
-        (-170., 70.), (179., 70.)
+        (-170., 70.), (179., 70.),
     ])
     assert not polygon.exterior.is_ccw
     polygons = list(split_polygon_on_antimeridian_ccw(polygon))
@@ -200,7 +243,7 @@ def test_split_polygon_on_antimeridian_ccw_close_point():
     polygon = Polygon([
         (179.999999, 70.),
         (179., 60.), (-170., 60.),
-        (-170., 70.), (179., 70.)
+        (-170., 70.), (179., 70.),
     ])
     assert not polygon.exterior.is_ccw
     polygons = list(split_polygon_on_antimeridian_ccw(polygon))
diff --git a/tests/test_transformer.py b/tests/test_transformer.py
index d792ddc..9f559f3 100644
--- a/tests/test_transformer.py
+++ b/tests/test_transformer.py
@@ -24,7 +24,7 @@ def test_from_wkt(simplify_transformer):
             (51.0, 21.0),
             (51.0, 20.0),
             (50.0, 20.0),
-        ])
+        ]),
     ]
     assert simplify_transformer.from_wkt(
         "POLYGON(( 1 1, 2 1, 1 2, 1 1))",
@@ -34,7 +34,7 @@ def test_from_wkt(simplify_transformer):
             (2, 1),
             (1, 2),
             (1, 1),
-        ])
+        ]),
     ]
     # Duplicate point is removed
     assert simplify_transformer.from_wkt(
@@ -46,14 +46,14 @@ def test_from_wkt(simplify_transformer):
             (51.0, 21.0),
             (51.0, 20.0),
             (50.0, 20.0),
-        ])
+        ]),
     ]
 
 
 def test_from_wkt_multipolygon(simplify_transformer):
     assert simplify_transformer.from_wkt(
         "MULTIPOLYGON (((30 20, 45 40, 10 40, 30 20)),"
-        "((15 5, 40 10, 10 20, 5 10, 15 5)))"
+        "((15 5, 40 10, 10 20, 5 10, 15 5)))",
     ) == [
         Polygon([
             (30.0, 20.0),