This book is a fantastic introduction to game theory where the authors are cleverly worried about the algorithms used to solve the problems. Therefore, it provides a great link among computer science, economic theory and operational research.
The structure of the book is based on very clear definitions, elucidating examples and theorems (not all proved, but several ones are proved). A great point of the book is the updated list of references in the last section of each chapter that can help the interested the reader find additional information about each topic is being taught in the book.
Chapter 1 introduces the problem of Distributed constraint satisfaction that will be used later in the book to compute the Nash equilibrium.
Chapter 2 is a basic introduction to dynamic programming and auction theory.
Chapters 3, 4 and 5 provide an introduction to decision theory and basic game theory. The bonus of these chapters is the list of algorithms that are presented in order to compute the equilibriums. It is worth mentioning that these chapters are as good as the best available introductions to game theory. All the basic topics are clearly covered.
Chapter 6 presents more specific representations of games. Some of them are very common in other books (such as Repeated games and Bayesian games), but others (such as congestion games) are not very common.
Chapter 7 deals with learning and teaching. The main topics of this chapter are two very uncommon topics in game theory books, namely reinforcement learning (you may find for instance in the fantastic book of Suton and Barto or Bertsekas) and evolutionary game theory (you may find in Game theory evolving - Gints, Evolutionary game theory - Weibull, Evolutionary Games and Population Dynamics - Hofbauer and Sigmund, but not the most common books of game theory).
Chapter 8 is about communication. This is a very interesting presentation of the topic Doing by talking (cheap talk) X Talking by doing (signaling games). Furthermore, an unusual topic of this chapter is presentation of the speech act theory dealing with rules of conversation and game theoretical view of speech acts.
Chapter 9 is about the difficult to aggregate preferences.
Chapter 10 is a clever introduction to mechanism design.
Chapter 11 is a very good introduction to auctions.
Chapter 12 presents coalitional game theory. This topic may be found for instance in A Course in Game Theory - Martin J. Osborne and Ariel Rubinstein, but the presentation in Osborne and Rubinstein is much more demanding.
Chapter 13 and 14 is about the logics of knowledge and belief.
Summarizing... This book is not another introduction to game theory, it is much more. It presents a lot of topics not common in other introductions and also presents several useful algorithms. Furthermore, it presents a good balance between mathematics and intuition.