In Search of the Multiverse
The book starts with a look at the Everett interpretation of quantum theory, but doesn't stop there. Gribbin goes on to look at how an infinite universe may be considered as a collection of infinitely many individual universes. He also examines how universes might reproduce themselves, via mechanisms such as eternal inflation or even via intelligent beings in one universe creating new universes. Antropic arguments - in such a large collection of universes, some must be right for life - are a significant theme of the book.
It's important to be clear that this is highly speculative stuff, rather than a layman's account of Many Worlds quantum theory. There's nothing wrong with speculation, but personally I would rather hear about it directly from those who come up with the ideas. I'm also going off anthropic arguments, so this book didn't really suit me, and I wouldn't see it as a winner of the 2010 Royal society science book prize. However, others might get more out of it, as it does provide an easy to read introduction to a lot of interesting new ideas.