The purpose of this book is to give a detailed account of some recent devel- ments in the ?eld of probability and statistics for dependent data. It covers a wide range of topics from Markov chains theory, weak dependence, dynamical system to strong dependence and their applications. The title of this book has been somehow borrowed from the book Dependence in Probability and Statistics: a Survey of Recent Result edited by Ernst Eberlein and Murad S. Taqqu, Birkh] auser (1986), which could serve as an excellent prerequisite for reading this book. We hope that the reader will ?nd it as useful...