RATIONALE Tremendous progress has been made in the areas of quantum computing and quantum information theory during the past decade. Thousands of research papers, a few solid reference books, and many popular science books have been published in recent years on this subject. The growing interest in quantum computing and quantum information theory is motivated by the incredible impact these disciplines are expected to have on how we store, process, and transmit data and knowledge in this information age. Computer and communication systems using quantum effects have remarkable properties. Quantum computers enable efficient simulation of the most complex physical systems we can envision. Quantum algorithms allow efficient factoring of large integers with applications to cryptography. Quantum search algorithms considerably speed up the process of identifying patterns in apparently random data. We can guarantee the security of our quantum communication systems because eavesdropping on a quantum communication channel can be detected with high probability. It is true that we are years, possibly decades, away from building a quantum computer requiring little, if any power at all, filling up the space of a grain of sand, and computing at speeds that are unattainable today even by covering tens of acres of floor space with clusters made from tens of thousands of the fastest processors built with current state-of-the-art solid-state technology. All we have at the time of this writing is a 7-qubit quantum computer capable of computing the prime factors of a small integer, 15 139. To break a code with a key size of 1024 bits requires more than 3000 qubits and 108 quantum gates 82. Building a quantum computer presents tremendous technological and theoretical challenges. At the same time, we are witnessing a faster rate of progress in quantum information theory than in quantum computing. Applications of quantum cryptography seem ready for commercialization. Recently, a successful quantum key distribution experiment over a distance of some 100 km has been announced. It is difficult to predict how much time will elapse from the moment of a great discovery until it materializes into a device that profoundly changes our lives or drastically affects our understanding of natural phenomena. The first atomic bomb was detonated in 1945, less than 10 years after the discovery of nuclear fission by Lise Meitner and Otto Hahn 91. The first microprocessor was built in late 1970s, some 30 years after the creation of the transistor on December 23, 1947 by William Shockley, John Bardeen, and Walter Brattain. Francis Harry Compton Crick and James Dewey Watson discovered the double helix structure of the genetic material in 1957 and the full impact of their discovery will continue to reverberate for years to come. The authors believe that the time to spread the knowledge about quantum computing and quantum information outside the circle of quantum computing researchers and students majoring in physics is ripe. Students and professionals interested in information sciences need to adopt a different way of thinking than the one used to construct today's algorithms. This certainly presents tremendous challenges, since, for many years, computer science students have been led to believe that they can get by with some knowledge of discrete mathematics and little understanding of physics at all. We are going back to the age when a strong relationship between physics and computer science existed. TOPICS, PREREQUISITES, AND CHAPTER DESCRIPTIONS This text is devoted to quantum computing. We treat the quantum computer as a mathematical abstraction. Yet, we discuss in some depth the fundamental properties of a quantum system necessary to understand the subtleties of counterintuitive quantum phenomena such as entanglement. Chapter 1 introduces the reader to the quantum world by way of several experiments. Chapter 2 providesDan C. Marinescu is the author of 'Approaching Quantum Computing', published 2004 under ISBN 9780131452244 and ISBN 013145224X.