This study is geared toward undergraduate students in their junior and senior years. It contains several examples, sets of problems, exercises that have been solved, and sections of abstract algebra that apply to many different subfields of discrete mathematics. Even though this is a mathematics book, the authors have made a significant effort to cater to the requirements of users who intend to use the methods covered.

There are over 500 exercises spread out among the 40 different sections of this book that support the fully worked out computational examples. In this updated edition, there is a new chapter on cryptology and an expanded chapter on applications of groups. In addition, a substantial chapter that surveys various applications that were not included in the original edition has been added. This book assumes that the reader is familiar with the concepts presented in a linear algebra class and, preferably, the material presented in an introductory (abstract) algebra class that covers the fundamentals of groups, rings, and fields.