We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Shastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its first version. While preparing this edition we made some clarifications in several sections and also corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “Effects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated reffect the most interesting results obtained by the authors after publication of the first edition. We hope that the new edition of the book will be of great interest for a wide section of readers who are already specialists or those who are beginning research in the fields of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and shastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition This book is devoted to the classical background and on temporary results on nonlinear dynamics of deterministic and shastic systems. Considerable attention is given to the effects of noise on various regimes of dynamic systems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium and shastic processes. This book is an attempt ombine the approach of nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on shastic or kineticequations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.