Business cycle theory has been one of the fastest growing fields in modern nonlinear economic dynamics. The book is centered around models of multiplier-accelerator type, emerging from Samuelson's seminal work, later developed into nonlinear formats by Hicks and Goodwin. These models left open ends, as the tools then available did not permit more systematic analysis. The present situation is different, due to the emergence of new methods also focusing global analysis. The focus on classical, causal or recursive models implies a deviation from current main stream business cycle theory, based on 'rational expectations', which in view of the possibility of mathematical chaos becomes untenable. This book is a rejoinder to Puu and Sushko, Oligopoly Dynamics - Models and Tools, (Springer 2002).