Due to advances in both theory and practice, there has been a recent explosion in courses on network science and data science. These demand a solid background in probabilistic methods.

For example, Markov chains are used for node ranking in complex networks, and data compression is used for minimization of communication in wireless networks. Therefore, books such as this one, which offer the necessary solid introduction along with more advanced material on probabilistic models and methods, are necessary for these courses.

This book’s 21 chapters describe generic models such as Markov chains, Erdos-Renyi (random) graphs, random walks on graphs, and Markov fields; include universal methods such as the Stein and martingale methods; and cover many useful tools such as the Chernoff, Hoeffding, and Holley inequalities. The first five chapters present basic material to make the book as self-contained as possible, although experience in calculus and linear algebra is necessary.

This book is an excellent piece of writing. It has the strictness of a mathematical book whose traditional purpose is to state and prove theorems, and also has the features of a book on an engineering topic, where solved and unsolved exercises are provided. I appreciated the very carefully selected solved examples that are interwoven in each chapter. They provide an indispensable aid to digest the concepts and methods presented.

Primarily, the book targets an audience whose focus is on the theory of probability. Advanced undergraduate or graduate students are the book’s two main audiences. However, I firmly believe that the book is equally useful for computer scientists and engineers, communication engineers, and moreover physicists. For instance, the chapters on Markov chains are among the main reasons for the book’s relevance to many disciplines.

Other phenomena such as percolation and phase transition, encountered mainly in physics and in the study of networks, can also be explained using probability models.

Overall, the book is a valuable addition to the arsenal of students and professionals in their battle to understand and scientifically model the world.