The book claims to be a successor of Prof. Bollobas' book of the same title. Unlike Prof. Bollobas' book, I do not think this one is a very good textbook: The proofs of many theorems are not given, but the reader is directed to some source; these theorems are not of some unrelated subject, but their topic is random graphs. These unproven theorems are then used in the sequel to prove other theorems.
Furthermore, many proofs are delegated to "Excercises!", but no solutions are given.
Thirdly (at least for me, I am not a professional mathematician), the presentation is at very uneven levels: Very easy derivations and extremely hard derivations are mixed together, it seems the authors have little feel for the difficulty of their exposition.

On the positive side: The book is vitually typo-free, and the section on inequalities is much clearer -actually very good!- than the one in Prof. Bollobas's book.

A curious aside: two pages (pages 180, 181) were simply missing, and they were also missing in a second copy I ordered. Neither Amazon, nor the publisher (Wiley) were of any help getting those two pages.