Book recommendations on cellular automata?

First, there is an unannotated list of books on cellular automata here. Second, if you are going to get just one book, then I think it has to be Wolfram's A New Kind of Science, which, despite its flaws, is the source of so much of the research in cellular automata that it must be confronted first. [I see I am concuring with Kevin O'Bryant's just-posted recommendation.] You might read the review by Lawrence Gray in the Notices of the American Mathematical Society (February 2003) to make yourself aware of the controversies surrounding this book. If you can overlook its flaws, it is a remarkable book, and quite fun to work through.

There's a Cellular Automata and Groups by Ceccherini-Silberstein in Springer Monographs in Mathematics. It's self-contained and introduce the CA with group theory.

I know the flames are coming, but I can't stop myself. You might enjoy "A new kind of science", by Stephen Wolfram. It's available free online, and has quite a bit of code and quite a few fun experiments inside.