Book Description: From the Preface: ``The purpose of our book is to provide an overall view of all the basic features of almost periodic functions, in the various meanings this term has acquired in modern research as well as the many applications of such functions. This feature of the book should, of course, make it useful to those readers who are interested in the connections that exist between theory (pure!) of almost periodic functions and such areas of application as the theory of ordinary differential equations and partial differential equations. Several other areas of application are also indicated, together with an abundance of references. The Bibliographical Notes at the end of almost every chapter have been added to in this Second Edition. Completely new is [Chapter II.3], which is devoted to a relatively new class of almost periodic functions: random functions almost periodic in probability. It is certain that these functions will find many applications in the theory of stochastic functional equations.''