This book is devoted to quantum computing, a new, multidisciplinary research area crossing quantum mechanics, theoretical computer science and mathematics. It contains an introduction to quantum computing as well as the most important recent results on the topic. Two famous algorithms, fast factorization and Grover search, are presented in separate chapters because these inventions are important structurally and developmentally.The presentation of the topic is uniform and computer science-oriented. Thus, the book differs from most of the previous ones which are mainly physics-oriented. The special style of presentation makes the theory of quantum computing accessible to a larger audience, including also the mathematics-oriented readers. Many examples and exercises ease the understanding.In this edition a new chapter on quantum information has been added, and numerous corrections, amendments and extensions have been incorporated throughout the text.