Book on advanced discrete probability? Searching for materials on discrete probability I find "first course in probability" type stuff and some seemingly rather specific things. Is there a principled, step-by-step introduction to advanced discrete probabilistic topics (e.g. in a book)? Are there any advanced general theorems in this area at all?

Discrete Probability Models and Methods, by Pierre Brémaud (Springer). Quoting from the introduction to the book:

The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. [...]
The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.

