Feel free to suggest more books! If they are interesting, I will read them, review them and put on the list.
Learning AndEngine - This is my own book. It is written in the same style as my tutorials with more details. It is meant for complete beginners with a basic Java understanding. It teaches how to make a full doodle-jump style game in AndEngine. You will also learn where to get free resources and how to publish a game to Google Play Store.
AndEngine for Android Game Development Cookbook - Everybody who takes AndEngine game development seriously should read this book. Not only it shows you plenty of useful recipes and hints, but it also gives you an opportunity to study source code of a simple but polished and well written game.
General Android and game development
Unity Android Game Development by Example Beginner's Guide - If you are a beginner in Android game development and want to learn Unity, pick this book. It covers basics and it will give you four complete games with source codes and all assets to learn from. Perfect for people who don't like theory and prefer hands-on excercises.
Developing Beautiful Android Live Wallpapers (Make Money on Android) - There are not many resources on live wallpaper development, so this little book might come handy. Written by a member of the AndEngine community.