Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular, their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. This book comprehensively covers all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. The text is based on courses taught successfully over many years at the University of Michigan, Imperial College, London and Pennsylvania State University. "The monograph is a very readable, concise presentation of classical prime number theory, giving techniques as well as the underlying ideas, and describing an incredibly large range of topics. A study of this monograph seems to be a must for every number theorist. Hopefully this volume will be available as soon as possible, to renew and broaden the interest in this highly interesting field of analytic prime number theory." Wolfgang Schwarz, Mathematical Reviews A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.