The analysis of time series data has for many years been a central component of statistical research and practice and the theory of linear time series is now well-established. However, the theory of non-linear time series is still a rapidly developing subject. This book is an introduction to some of these developments and the present state of research. It is a theme of this book that developments in the study of dynamical systems have motivated many of the advances covered here. Consequently, Professor Tong discusses in some detail the fundamental concepts of dynamical systems theory such as limit cycles, Lyapunov exponents, thresholds, and stability, and demonstrates their role in the analysis of non-linear time series. The result is a book which provides the first accessible and comprehensive account of these exciting new developments and bridges the gap between linear and chaotic time series analysis. Both statisticians and dynamical system theorists will benefit from this account of the interplay between their subjects and the author has included discussions of many of the outstanding open problems which remain. As a companion to this book, a microcomputer software package is available for the testing for nonlinearity and the fitting of threshold autoregressive models. For more information, please contact the author.