This book is a general inquiry into the effects of nonlinearity on dynamic economic models, focusing phenomena such as limit cycles, quasiperiodicity, bifurcations, and chaos. Topics from both micro- and macroeconomics are dealt with, for instance the search dynamics of a monopolist facing multiple optima, the dynamics of Cournot oligopoly, and, above all, business cycle theory, including mostly original research results. Models in discrete time as well as in continous time are focused, and this completely rewritten fourth edition is provided with an extensive mathematical introduction, dealing with both differential equations, and with discrete maps, so making the book selfcontained, and even explaining tools such as perturbation methods or the computation of Lyapunov exponents.