The book took me probably two or three attempts to 'get into' it. It was hard going at times, and a number of times i had to get a pencil and paper out to work through and make sure that i deeply understood the text. That said, the quality of the what's written is, i have no doubt, precise (in a mathematical context) and once you get used to the way Binmore writes is good. (although i understand that's a big ask)
Despite being hard going at times, it also had it's moments of absolute clarity. He goes through a broad range of topics: What a 'game' is in a mathematical sense; effect of chance, time, repeated games and the effect that has on players perception of strategy; Information, and what players can learn about the other players based on what they do; Auctions; Evolutionary Biology (very interesting), and how game theory can accurately predict/explain why animals do some actions, or why people are altruistic or why people would put themselves in harms way to save others. Bargaining and coalitions (not my personal favourite) and a short section on puzzles and paradoxes at the end, which it thought was a nice way to round off a book like this.
As the book goes, Binmore also give the reader a history of game theory, so that they can appreciate the development of this branch of mathematics. I enjoyed this as it meant that i could piece together how this reletively new branch came into being and how its developed to today.
For me the major downside of some of this book is the way that it has been explained in a non-intuitive way, and some of it really does make to struggle and want to throw the book as hard as you can across the room and scream. However, like most pieces of mathematics, if you work at it and follow the reasoning through, you see why it has been written in such a convoluted way - precision. Some people might not like the idea that you have to 'work' with this book and to a point I agree, but this book isn't called "Game Theory; In simple terms" it's called "Game Theory: A Very Short Introduction" it's there to introduce you to it and to get a good grasp of the subject you'll have to work with it. And if you do, i'm sure you'll love it.
:)