The book provides a comprehensive survey of modern business cycle theory. Starting with the empirically relevant question of measuring business cycles, it encompasses shock-dependent and shock-independent business cycle models. The book attempts to familiarize the reader with mathematical tools like linear difference and differential equations, the Poincaré-Bendixson theorem or predator-prey systems and illustrates the usage of these tools by presenting rational expectation models, disequilibrium models with rationing, and other basic approaches. A separate chapter is devoted to new developments in dynamical economics and their relevance to business cycle theory. The Hopf bifurcation, chaos and catastrophe theory are shortly surveyed and illustrated by simple examples of common business cycle theory. The new edition has been revised and enlarged. It includes a presentation of the Smithies model and recent developments in nonlinear time series analysis.