The book under review shows the reader a variety of techniques and tools used in analytic number theory. It covers a broad spectrum of topics starting with results on arithmetic functions and the elementary theory of prime numbers, through classical results of analytic number theory on L-functions, and primes in arithmetical progression or the circle method, to more modern parts such as sieve methods, Kloosterman sums, sums over finite fields or automorphic forms. The book is written in a very lively and nicely readable style, and requires only standard prerequisites from real and complex calculus or the theory of Fourier series. It is intended for graduate students but could be very useful for everyone who is interested in many facets of methods of analytic number theory. In particular, the book contains very well chosen and balanced material.