The fascicles in this volume describe many important aspects of combinatorics, including algorithms, binary decision diagrams, history, combinations, partitions, tuples, and permutations. The most important feature is the extensive number of diverse, in-depth problems contained in the fascicles; Knuth not only provides answers to the problems, but also describes how the results came about, including bibliographical references where appropriate (that is, when the answer was not found by Knuth himself). It is important to emphasize the advanced level of the exercises, for the following reason: although Knuth very carefully explains the theory, in a very entertaining and pedagogical way, most students are expected to have mastered combinatorics and calculus, at the very least, at the level of Finite mathematics [1] and Advanced calculus [2].

Knowledge from one of Knuth’s previous books [3] is also a prerequisite, since several machine language programs are based on this protocol. For solving several of the problems, it is necessary to download some files from the Stanford GraphBase Web page [4].

I recommend this book to advanced students, mathematicians, and researchers in the fields of computer science, finite mathematics, probability theory, and related subjects.