diff --git a/.github/workflows/main.yml b/.github/workflows/main.yml
new file mode 100644
index 0000000000..fcdcb905d1
--- /dev/null
+++ b/.github/workflows/main.yml
@@ -0,0 +1,64 @@
+name: CI
+on: [push, pull_request]
+
+jobs:
+  test:
+    name: Run tests
+    runs-on: ubuntu-latest
+    steps:
+    - uses: actions/checkout@master
+    - name: Update rustup
+      run: rustup self update
+    - name: Install Rust
+      run: |
+        rustup set profile minimal
+        rustup toolchain install 1.41.0 -c rust-docs
+        rustup default 1.41.0
+    - name: Install mdbook
+      run: |
+        mkdir bin
+        curl -sSL https://github.com/rust-lang/mdBook/releases/download/v0.3.5/mdbook-v0.3.5-x86_64-unknown-linux-gnu.tar.gz | tar -xz --directory=bin
+        echo "##[add-path]$(pwd)/bin"
+    - name: Report versions
+      run: |
+        rustup --version
+        rustc -Vv
+        mdbook --version
+    - name: Run tests
+      run: mdbook test
+  lint:
+    name: Run lints
+    runs-on: ubuntu-latest
+    steps:
+    - uses: actions/checkout@master
+    - name: Update rustup
+      run: rustup self update
+    - name: Install Rust
+      run: |
+        rustup set profile minimal
+        rustup toolchain install nightly -c rust-docs
+        rustup default nightly
+    - name: Install mdbook
+      run: |
+        mkdir bin
+        curl -sSL https://github.com/rust-lang/mdBook/releases/download/v0.3.5/mdbook-v0.3.5-x86_64-unknown-linux-gnu.tar.gz | tar -xz --directory=bin
+        echo "##[add-path]$(pwd)/bin"
+    - name: Report versions
+      run: |
+        rustup --version
+        rustc -Vv
+        mdbook --version
+    - name: Spellcheck
+      run: bash ci/spellcheck.sh list
+    - name: Lint for local file paths
+      run: | 
+        mdbook build
+        cargo run --bin lfp src
+    - name: Validate references
+      run: bash ci/validate.sh
+    - name: Check for broken links
+      run: |
+        curl -sSLo linkcheck.sh \
+          https://raw.githubusercontent.com/rust-lang/rust/master/src/tools/linkchecker/linkcheck.sh
+        # Cannot use --all here because of the generated redirect pages aren't available.
+        sh linkcheck.sh book
\ No newline at end of file
diff --git a/.travis.yml b/.travis.yml
deleted file mode 100644
index 5221c0edf7..0000000000
--- a/.travis.yml
+++ /dev/null
@@ -1,18 +0,0 @@
-sudo: false
-dist: trusty
-language: rust
-cache: cargo
-rust:
-  - 1.41.0
-branches:
-  only:
-  - master
-addons:
-  apt:
-    packages:
-      - aspell
-      - aspell-en
-before_script:
-  - (cargo install mdbook --vers 0.3.5 --force || true)
-script:
-  - bash ci/build.sh
diff --git a/ADMIN_TASKS.md b/ADMIN_TASKS.md
index ad02693a33..701375574b 100644
--- a/ADMIN_TASKS.md
+++ b/ADMIN_TASKS.md
@@ -5,7 +5,7 @@ occasional maintenance tasks.
 
 ## Update the `rustc` version
 
-- Change the version number in `.travis.yml`
+- Change the version number in `.github/workflows/main.yml`
 - Change the version number in `rust-toolchain`, which should change the version you're using
   locally with `rustup`
 - Change the version number in `src/title-page.md`
diff --git a/README.md b/README.md
index 08d53c8423..5f86f89a3d 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # The Rust Programming Language
 
-[![Build Status](https://travis-ci.com/rust-lang/book.svg?branch=master)](https://travis-ci.com/rust-lang/book)
+![Build Status](https://github.com/rust-lang/book/workflows/main/badge.svg)
 
 This repository contains the source of "The Rust Programming Language" book.
 
diff --git a/ci/validate.sh b/ci/validate.sh
new file mode 100644
index 0000000000..9e2cfdf10d
--- /dev/null
+++ b/ci/validate.sh
@@ -0,0 +1,4 @@
+for file in src/*.md ; do
+    echo Checking references in $file
+    cargo run --quiet --bin link2print < $file > /dev/null
+done
\ No newline at end of file