The volume consists of more than twenty papers covering all important areas of the contemporary research in dynamical systems. The contributing authors belong to leading experts in the field, and the articles, though mostly of expository nature, are also of high scientific level. The book is formally divided into two parts. In the first part we can read, among others, about mixing, entropy, ergodic theory, symbolic dynamics, averaging, normal forms and rigidity theory. The second part is devoted to topics connected with hyperbolic dynamics. The volume is dedicated to Anatole Katok on the occasion of his 60th birthday. The volume starts with an introductory article (written by the editors) describing shortly his life and scientific work.