Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has now been made, particularly during the past two decades. The three volumes that make up Noise in nonlinear dynamical systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. It is anticipated that this work will help to stimulate new research, and that it will be of value to all those entering or already working in the field by bringing together all the experimental and theoretical tools needed. The books will be of interest not only to researchers in statistical physics, but also to those people working in relevant areas of chemistry, engineering and biology. and many other branches of science and technology. The first volume deals with the basic theory of stochastic nonlinear systems. It includes an historical overview of the origins of the field, chapters covering recently developed theoretical techniques for the study of coloured noise, and the first English language translation of the landmark 1933 paper by Pontriagin, Andronov and Vitt.