diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index d0189db14..fc5733ba0 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -12,7 +12,6 @@ jobs:
   build-and-test:
     name: "Python ${{ matrix.python-version }} on ${{ matrix.os }} jax=${{ matrix.jax-version }}"
     runs-on: "${{ matrix.os }}"
-
     strategy:
       matrix:
         python-version: ["3.9", "3.10", "3.11"]
@@ -22,7 +21,6 @@ jobs:
           - python-version: "3.9"
             os: "ubuntu-latest"
             jax-version: "0.4.27"  # Keep version in sync with pyproject.toml and copy.bara.sky!
-
     steps:
       - uses: "actions/checkout@v2"
       - uses: "actions/setup-python@v4"
@@ -33,13 +31,72 @@ jobs:
       - name: Run CI tests
         run: JAX_VERSION="${{ matrix.jax-version }}" bash test.sh
         shell: bash
+  doctests:
+    name: "Doctests on ${{ matrix.os }} with Python ${{ matrix.python-version }}"
+    runs-on: "${{ matrix.os }}"
+    strategy:
+      matrix:
+        python-version: ["3.11"]  # only build docs with a somewhat latest python
+        os: [ubuntu-latest]
+    steps:
+      - uses: "actions/checkout@v2"
+      - uses: "actions/setup-python@v4"
+        with:
+            python-version: "${{ matrix.python-version }}"
+            cache: "pip"
+            cache-dependency-path: 'pyproject.toml'
+      - name: Build docs and run doctests
+        run: |
+          python3 -m pip install --quiet --editable ".[docs]"
+          cd docs
+          make html
+          make doctest # run doctests
+        shell: bash
+  linting:
+    name: "Lint check with flake8 and pylint"
+    runs-on: "ubuntu-latest"
+    steps:
+      - uses: "actions/checkout@v2"
+      - uses: "actions/setup-python@v4"
+        with:
+            python-version: "3.11"
+            cache: "pip"
+            cache-dependency-path: "pyproject.toml"
+      - name: Install linting dependencies
+        run: |
+          pip install -U pip setuptools wheel
+          pip install -U flake8 pytest-xdist pylint pylint-exit
+      - name: Lint with flake8
+        run: |
+          python3 -m flake8 --select=E9,F63,F7,F82,E225,E251 --show-source --statistics
+      - name: Lint module files with pylint
+        run: |
+          PYLINT_ARGS="-efail -wfail -cfail -rfail"
+          python3 -m pylint --rcfile=.pylintrc $(find optax -name '*.py' | grep -v 'test.py' | xargs) -d E1102 || pylint-exit $PYLINT_ARGS $?
+      - name: Lint test files with pylint
+        run: |
+          PYLINT_ARGS="-efail -wfail -cfail -rfail"
+          python3 -m pylint --rcfile=.pylintrc $(find optax -name '*_test.py' | xargs) -d W0212,E1102 || pylint-exit $PYLINT_ARGS $?
+  ruff-lint:
+    name: "Lint check with ruff"
+    runs-on: "ubuntu-latest"
+    steps:
+      - uses: "actions/checkout@v2"
+      - uses: "actions/setup-python@v4"
+        with:
+            python-version: "3.11"
+            cache: "pip"
+            cache-dependency-path: "pyproject.toml"
+      - name: Install ruff and lint check
+        run: |
+          pip install -U ruff
+          ruff check .
   markdown-link-check:
     name: "Check links in markdown files"
     runs-on: "ubuntu-latest"
     steps:
     - name: Checkout repository
       uses: actions/checkout@v4
-
     - name: Check links
       uses: gaurav-nelson/github-action-markdown-link-check@v1
       with:
diff --git a/examples/contrib/reduce_on_plateau.ipynb b/examples/contrib/reduce_on_plateau.ipynb
index 4187947ad..05e3d9c2b 100644
--- a/examples/contrib/reduce_on_plateau.ipynb
+++ b/examples/contrib/reduce_on_plateau.ipynb
@@ -372,7 +372,7 @@
       "source": [
         "opt = optax.chain(\n",
         "    optax.adam(LEARNING_RATE),\n",
-        "    reduce_on_plateau(\n",
+        "    contrib.reduce_on_plateau(\n",
         "        patience=PATIENCE,\n",
         "        cooldown=COOLDOWN,\n",
         "        factor=FACTOR,\n",
@@ -759,7 +759,7 @@
         }
       ],
       "source": [
-        "transform = reduce_on_plateau(\n",
+        "transform = contrib.reduce_on_plateau(\n",
         "    patience=PATIENCE,\n",
         "    cooldown=COOLDOWN,\n",
         "    factor=FACTOR,\n",
diff --git a/examples/linear_assignment_problem.ipynb b/examples/linear_assignment_problem.ipynb
index e994f00bd..f77d62477 100644
--- a/examples/linear_assignment_problem.ipynb
+++ b/examples/linear_assignment_problem.ipynb
@@ -55,7 +55,7 @@
    "outputs": [],
    "source": [
     "import networkx as nx\n",
-    "from jax import numpy as jnp, random\n",
+    "from jax import random\n",
     "import optax\n",
     "from matplotlib import pyplot as plt"
    ]
diff --git a/examples/nanolm.ipynb b/examples/nanolm.ipynb
index b098b69c9..f34db019c 100644
--- a/examples/nanolm.ipynb
+++ b/examples/nanolm.ipynb
@@ -629,7 +629,7 @@
         }
       ],
       "source": [
-        "plt.title(f\"Convergence of adamw (train loss)\")\n",
+        "plt.title(\"Convergence of adamw (train loss)\")\n",
         "plt.plot(all_train_losses, label=\"train\", lw=3)\n",
         "plt.plot(\n",
         "    jnp.arange(0, len(all_eval_losses) * N_FREQ_EVAL, N_FREQ_EVAL),\n",
diff --git a/optax/schedules/_inject.py b/optax/schedules/_inject.py
index 43bd2feef..2eb19e945 100644
--- a/optax/schedules/_inject.py
+++ b/optax/schedules/_inject.py
@@ -30,7 +30,7 @@
 
 def _convert_floats(x, dtype):
   """Convert float-like inputs to dtype, rest pass through."""
-  if jax.dtypes.scalar_type_of(x) == float:
+  if jax.dtypes.scalar_type_of(x) is float:
     return jnp.asarray(x, dtype=dtype)
   return x
 
diff --git a/pyproject.toml b/pyproject.toml
index 7bccb6db3..3b01fa880 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -87,3 +87,17 @@ dp-accounting = [
 [tool.setuptools.packages.find]
 include = ["README.md", "LICENSE"]
 exclude = ["*_test.py"]
+
+[tool.ruff.lint]
+select = [
+    "F",
+    "E",
+]
+ignore = [
+    "E731",  # lambdas are allowed
+    "E501",  # don't check line lengths
+    "F401",  # allow unused imports
+    "E402",  # allow modules not at top of file
+    "E741",  # allow "l" as a variable name
+    "E703",  # allow semicolons (for jupyter notebooks)
+]
diff --git a/test.sh b/test.sh
index e6d258535..f387d95bc 100755
--- a/test.sh
+++ b/test.sh
@@ -101,4 +101,7 @@ make html
 make doctest # run doctests
 cd ..
 
+pip install -U ruff
+ruff check .
+
 echo "All tests passed. Congrats!"