This textbook on the theory of nonlinear dynamical systems for nonmathematical advanced undergraduate or graduate students is also a reference book for researchers in the physical and social sciences. It provides a comprehensive introduction including linear systems, stability theory of nonlinear systems, bifurcation theory, chaotic dynamics. Discussion of the measure--theoretic approach to dynamical systems and the relation between deterministic systems and stochastic processes is featured. There are a hundred exercises and an associated website provides a software program, computer exercises and answers to selected book exercises V. 3. Front Matter -- Colour Plates -- The Chaos Computing Paradigm / William L Ditto, Abraham Miliotis, K Murali, Sudeshna Sinha -- How Does God Play Dice? / Jan Nagler, Peter H Richter -- Phase Reduction of Stochastic Limit-Cycle Oscillators / Kazuyuki Yoshimura -- Complex Systems, Numbers and Number Theory / Lucas Lacasa, Bartolo Luque, Octavio Miramontes -- Wave Localization Transitions in Complex Systems / Jan W Kantelhardt, Lukas Jahnke, Richard Berkovits -- From Deterministic Chaos to Anomalous Diffusion / Rainer Klages -- Index -- Reviews of Nonlinear Dynamics and Complexity