The required book is: Hello Android (3rd edition), by Ed Burnette, ISBN-13: 978-1934356562
Other useful books:
Android Wireless Application Development (2nd Edition), by Shane Conder and Lauren Darcey, ISBN-13: 978-0321743015
Android in Action (3rd edition), by Frank Ableson, Robi Sen, Chris King and C. Enrique Ortiz, ISBN-13: 978-1617290503
Android for Programmers: An App-Driven Approach, by by Paul J. Deitel, Harvey M. Deitel, Abbey Deitel and Michael Morgano, ISBN-13: 978-0-13-212136-1
Online Resources: (Not surprisingly there are a host of online resources for Android Development)
Main Android dev page: http://developer.android.com/index.html
Android developers Guide: http://developer.android.com/guide/index.html
Android library / API documentation: http://developer.android.com/reference/packages.html
Android Resources main page: http://developer.android.com/resources/index.html
Android Tutorials from Google: http://developer.android.com/resources/browser.html?tag=tutorial
Various pages on Android Topics: http://developer.android.com/resources/topics.html
Android Common Tasks: http://developer.android.com/resources/faq/commontasks.html
Android at Stack Overflow: http://stackoverflow.com/questions/tagged/android