Group theoretic problems appear to be the most promising source of hard computational problems for deploying new cryptographic constructions. This reference focuses on the specifics of using nonabelian groups in the field of cryptography. It provides an introduction to cryptography (mostly asymmetric) with a focus on group theoretic constructions, making it the first book to use this approach. The authors include all of the needed cryptographic and group theoretic concepts. They supply exercises at the end of each chapter, selected solutions in the back of the book, and suggestions for student projects that require the use of the computer or computer algebra systems.