The design and construction of the quantum computer is one of the most exciting and challenging goals of the scientific community. This book provides an introductory yet comprehensive treatment of the mathematical theory underlying quantum computation. The author adopts the formal, axiomatic style of stating and proving lemmas, propositions, and theorems, but does so in a way that keeps the treatment self-contained and accessible to a broad, multidisciplinary audience. Numerous diagrams of circuits and devices support the text. Plentiful exercises and examples reinforce the concepts and make this book suitable for graduate-level course work as well as a valuable reference for researchers and practitioners.