Second edition of the successful textbook which has emerged from a lecture series. The compact introduction addresses graduate students with a reasonably good background in physics, notably in quantum mechanics, plus some knowledge in introductory statistical mechanics and solid-state physics. The authors explain basic concepts from quantum mechanics and computer science which are used throughout the whole field of quantum computing and quantum communication. This second edition reflects the rapid development of the main ideas and techniques, e.g. by including the most recent experiments on cold atoms.