This volume presents a comprehensive introduction to the study of topological transformation groups, with respect to topological problems which can be traced back to the qualitative theory of differential equations. It provides a systematic exposition of the fundamental methods and techniques of abstract topological dynamics. The contents can be divided into two parts. The first part is devoted to a broad overview of the topological aspects of the theory of dynamical systems (including shift systems and geodesic and horocycle flows). Part 2 is more specialized and presents in a systematic way the fundamental techniques and methods for the study of compact minimal flows and their morphisms. It brings together many results which are scattered throughout the literature, and, in addition, many examples are worked out in detail. The primary purpose of this book is to bridge the gap between the beginner and the specialist in the field of topological dynamics. All proofs are therefore given in detail. The text should also be useful to the specialist and each chapter concludes with additional results (without proofs) and references to sources and related material. The prerequisites for studying the book are a background in general topology and (classical and functional) analysis.