The study of dynamical systems is a well established field applications in many disciplines. The authors have written this book in an attempt to provide a panorama of several aspects that are of interest to mathematicians and physicists alike. The book collects the material of several courses at the graduate level given by the authors. Thus, the exposition avoids detailed proofs in exchange for numerous illustrations and examples, while still maintaining sufficient precision. Apart from basic concepts in this field, a lot of attention is give to questions of physical measurement and stochastic properties of chaotic dynamical systems.