The 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. Unlike previous books which are mainly physics-oriented this book presents the topic in a computer science-oriented uniform way. This makes the theory of quantum computation accessible to a larger audience, including also the mathematics-oriented readers.