Since the ?rst edition of this book was published in 2001, the algebraic computa- ™ tion package Maple has evolved from Maple V into Maple 13. Accordingly, the second edition has been thoroughly updated and new material has been added. In this edition, there are many more applications, examples, and exercises, all with solutions, and new chapters on neural networks and simulation have been added. Therearealsonewsectionsonperturbationmethods,normalforms,Gröbnerbases, and chaos synchronization. This book provides an introduction to the theory of dynamical systems with the aid of the Maple algebraic manipulation package. It is written for both senior undergraduates and graduate students. The ?rst part of the book deals with c- tinuous systems using ordinary differential equations (Chapters 1–10 ), the second part is devoted to the study of discrete dynamical systems (Chapters 11–15), and Chapters 16–18 deal with both continuous and discrete systems. Chapter 19 lists examination-type questions used by the author over many years, one set to be used in a computer laboratory with access to Maple, and the other set to be used without access to Maple. Chapter 20 lists answers to all of the exercises given in the book. It should be pointed out that dynamical systems theory is not l- ited to these topics but also encompasses partial differential equations, integral and integro-differential equations, stochastic systems, and time delay systems, for instance. References [1]–[5] given at the end of the Preface provide more inf- mation for the interested reader.