This text is a high-level introduction to the modern theory of dynamical systems; an analysis-based, pure mathematics course textbook in the basic tools, techniques, theory and development of both the abstract and the practical notions of mathematical modelling, using both discrete and continuous concepts and examples comprising what may be called the modern theory of dynamics. Prerequisite knowledge is restricted to calculus, linear algebra and basic differential equations, and all higher-level analysis, geometry and algebra is introduced as needed within the text. Following this text from start to finish will provide the careful reader with the tools, vocabulary and conceptual foundation necessary to continue in further self-study and begin to explore current areas of active research in dynamical systems.

"This is a great introductory text for all students interested in the more mathematical aspects of nonlinear dynamics and chaos theory. I particularly recommend it to motivated students who consider specialising in dynamical systems theory. Whoever has mastered this book has an excellent overview of the modern understanding of the subject matter, has seen many interesting examples of various kinds of dynamical systems, and is well prepared to take up graduatelevel studies in this direction. Probably the author has written a new classic." - Thomas Peters, Contemporary Physics

"The book has over three hundred exercises integrated with the text. Very few are routine and several are pretty challenging. Overall this is a very attractive book" - William J. Satzer, Mathematical Association of America