The Busy Coder's Guide To Android Development
This article is from the original REM DEV blog (2008–2010). Some of the technologies it covers (Flex, Flash, AIR, JavaFX 1.x) have since been retired.
In my oppinion, this is the best introduction to Android for absolute beginners. The chapters on Android layouts and widgets are really good and easy to follow. Another interesting aspect of the book is that you can buy a subscription from the publisher (CommonsWare) and get access to all of its books (including updates) in electronic format. Considering how quickly Android is evolving, this could be well worth the investment.