This book is a systematic introduction to analytic methods in number theory, and assumes as a prerequisite only what is taught in a standard undergraduate course. The author aids readers by including a section of bibliographic notes and detailed exercises at the end of each chapter. Tenenbaum has emphasized methods rather than results, so readers should be able to tackle more advanced material than is included here. Moreover, he covers developments on many new and unpublished topics, such as: the Selberg-Delange method; a version of the Ikehara-Ingham Tauberian theorem; and a detailed exposition of the arithmetical use of the saddle-point method.