This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
A lot depends on one's background. Some who know Java very well, at least the core language, have a small head start. Android is its own world, though, with its own API and GUI widget set, etc. I'm not sure any knowledge from the J2EE world, or C#/.net, or Python or any other world gives any advantage. Myself, I come from 2D and 3D graphics, laboratory data acquisition, and scientific programming. Other than basic graphics concepts, none of that is any real advantages to learning Android. So I looked for books aimed at experienced programmers, but assuming no previous mobile experience and not assuming one is coming from any one specific realm of software development. The only bias I have is my interest is mostly in tablet apps not smartphone, and Android only not iOS or Blackberry or the other platforms.
Also, my reviews here may be skewed, because I don't consider myself a professional software developer or IT person in any sense, despite my actual work history, but rather I'm an "Artist/Physicist". Software is a tool, a means to an end. Maybe rarely I toy with software development for fun. Other software developers are likely to be hard core, doing it or aiming for it as a career, with both feet in the deep end of the pool, and know things that I don't. So be aware that my occasionally practised, self-educated, dilettante manner of software development influences my book choices.
I have three books at this time. Pick any two, I suppose. (Never rely totally on just one book for learning anything complex.)
* Beginning Android Tablet Application Development (in full color) - Wei Meng Lee. Somewhat cheap (compared to many SW dev books), not thick. This was a very good start to getting my first "hello world" level Android apps running. Good job explaining life cycle of Activities and Fragments, getting Eclipse to work properly, publishing apps.
* Android Programming Unleashed. B. M. Harwani. SAMS Special Edition sold through Barnes & Noble. Got it because it was bright orange and on sale at the time. Normally it would be overpriced, according to my wallet. Plenty of step by step examples, source code. But the writing is a bit lame - often just restating the obvious from the example source code. A few things weren't explained as well, but that could just be due to my brain likes the other authors' writing better. It had a few tidbits I didn't get from the Wei Meng Lee book. Have a look at it in the bookstore, and buy if it's appealing.
* Professional Android 4 Application Development, Reto Meier. Wrox Publishing. Very thick, plenty of detailed descriptions, tables of object properties, enums and such. I found this book too heavy on descriptive detail before getting to any do-it-yourself example coding. I'm one of those people who needs to take a swing at it before I'm ready to absorb more than the basic theory. But after I'm proficient at making at least basic Android Apps, this looks to be a very good resource, to use as reference if I can't get what I need from developer.android.com or some online forum. This book appears so in depth on many topics, I'll probably never even look at 30% of it. Android is a rich world with many aspects. There are interesting projects such as "Creating a Gravitational Force Meter" (to pick one at random) I'm eager to get to. This motivates me to master the basic stuff. I've always found Wrox to be good for thick books holding a lot of material, not necessarily for first-time learning, but for digging into various topics, getting a different author's viewpoint. A good supplement to books with immediate how-to satisfaction.
For all I know, all these books may be "obsolete" by now, but one has to start somewhere, and these books aren't old enough to not work.