ActionScript 3.0 Cookbook by Lott, Schall & Peters is an excellent book. This book allows you to quickly jump into AS3 Programming, as well as a nice reference for those items that need to be resolved quickly during the development process.
Each topic is grouped to provide information on specific problems so they can be accessed quickly and easily. This allows for the book to be used as a reference so you don’t have to read it from cover to cover…you could if you wanted to however. Along with each topic, this book provides many useful code examples. Not only that, but the authors explain why they used the code approach they did for that example.
That brings up another bonus point for this book; its simplicity. The book is extremely easy to understand. It does not however gloss over the more intricate points of a and goes into great detail without overwhelming the reader.
A few chapters to jump into are:
Chapter 8, The BitmapData chapter:
This chapter introduces the BitmapData class that was introduced in Flash 8, but is extremely usefully and simple to implement in Flex 2/Flash Player 9.
Chapter 6, the Display List chapter:
This chapter contains critical information on the rendering model in Flash Player 9, which has been completely re-designed
Chapter 20, the chapter on XML:
This chapter includes great information on dealing with XML in AS3, which has changed significantly from AS2 (say hi to e4x). This book explains most things you’ll need to do with XML in AS3.