Add Travis CI for Linux builds (clang/gcc)

diff --git a/.travis.yml b/.travis.yml
new file mode 100644
index 0000000..bec4a8e
--- /dev/null
+++ b/.travis.yml

@@ -0,0 +1,57 @@
+language: c
+
+os: linux
+
+matrix:
+  include:
+  - name: "GCC Debug"
+    compiler: gcc
+    addons:
+      apt:
+        packages:
+          - nasm
+    before_script:
+      - mkdir build
+      - cd build
+      - cmake -DCMAKE_BUILD_TYPE=Debug ..
+    script:
+      - make
+
+  - name: "GCC Release"
+    compiler: gcc
+    addons:
+      apt:
+        packages:
+          - nasm
+    before_script:
+      - mkdir build
+      - cd build
+      - cmake -DCMAKE_BUILD_TYPE=Release ..
+    script:
+      - make
+
+  - name: "Clang Debug"
+    compiler: clang
+    addons:
+      apt:
+        packages:
+          - nasm
+    before_script:
+      - mkdir build
+      - cd build
+      - cmake -DCMAKE_BUILD_TYPE=Debug ..
+    script:
+      - make
+
+  - name: "Clang Release"
+    compiler: clang
+    addons:
+      apt:
+        packages:
+          - nasm
+    before_script:
+      - mkdir build
+      - cd build
+      - cmake -DCMAKE_BUILD_TYPE=Release ..
+    script:
+      - make

diff --git a/README.md b/README.md
index d70879e..8ff8cd3 100644
--- a/README.md
+++ b/README.md

@@ -1,4 +1,4 @@
-# libavif [![AppVeyor Build Status](https://ci.appveyor.com/api/projects/status/github/joedrago/avif?branch=master&svg=true)](https://ci.appveyor.com/project/joedrago/avif)
+# libavif [![AppVeyor Build Status](https://ci.appveyor.com/api/projects/status/github/joedrago/avif?branch=master&svg=true)](https://ci.appveyor.com/project/joedrago/avif) [![Travis Build Status](https://travis-ci.com/joedrago/avif.svg?branch=master)](https://travis-ci.com/joedrago/avif)
 
 TBW