The first part of this book is an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations, both ordinary and partial, further with discrete maps, and with catastrophe theory. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, containing various applications in economics and in regional science. Coexistence of attractors and the multiplicity of development paths in nonlinear systems are central topics. The applications focus issues such as business cycles, oligopoly, interregional trade dynamics, and economic development theory, focusing increasing diversity and complexity. Some of the applications are cast as processes in discrete time, others are modelled in continuous time. Some have a layout involving even space and hence address issues of economic pattern formation in geographical space.