I have been looking for books on cellular automata, and I really can't afford more than one book right now, so I really need to make the right choice. What would be the right book for someone with a Computer Science Masters degree and also feels comfortable with Mathematical Logic and basic Abstract Algebra? (Or, to make the question more useful to others, what are the target readers of the most recent books 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 also "Cellular Automata Machines: A New Environment for Modeling" by Toffoli and Margolus.
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.
While Wolfram's A New Kind of Science (2002) is a beautifully-produced book and is lovely to look at, I find Wolfram's papers collected in Cellular Automata and Complexity (1994) much more informative. Because the papers were written for research publications they provide many of the technical details omitted from A New Kind of Science, which appears to have been written with a more general audience in mind.
You might also want to read Melanie Mitchell's review of A New Kind of Science. It appeared in the journal Science 298: 65-68. The review and Mitchell's insightful "Computation in Cellular Automata: A Selected Review" are available on her web page under "Publications."
I can't improve on the list in Joseph O'Rourke's answer, but I'd like to mention that Winning Ways gets on the list because of its discussion of Conway's "Life" cellular automaton. In particular Winning Ways outlines a proof that "Life" harbors a universal Turing machine. For more news on "Life" try this article, describing the recent discovery of a self-replicating pattern. The pattern is a little disappointing because it is destroyed in the process of making a copy of itself, but this leaves some interesting open problems:
"Another milestone might be a self-replicating pattern that creates increasing copies of itself, or a space-filling replicator that can make multiple copies to eventually fill an arbitrarily large area of the Life plane,"
This is a research list on evolving cellular automata - mostly stuff about finding CA rules with genetic algorithms but also CA only references.
Hope it helps.
Adamatzky's Game of Life Cellular Automata gives a fairly broad overview.
Aladjev V.Z. Classical Cellular Automata: Mathematical Theory and Applications.[Dash] Germany: Saarbrucken, Scholar`s Press, 2014, ISBN 9783639713459, 517 p.