With derivations, exercises, and solutions, this book examines the theoretical aspects of quantum computing and focuses on several candidates of a working quantum computer, evaluating them according to the DiVincenzo criteria. It covers theoretical tools, such as vectors, matrices, quantum gates, and integral and Fourier transforms. The book is very well structured and offers good theoretical explanations reinforced by examples. As the authors mention in the Preface, the book can be used for a quantum computing course. It is also recommended to advanced undergraduate students, postgraduate students and researchers in physics, mathematics and computer science.-Zentralblatt MATH 1185