The present book relies on various editions of my earlier book "Nonlinear Economic Dynamics", first published in 1989 in the Springer series "Lecture Notes in Economics and Mathematical Systems", and republished in three more, successively revised and expanded editions, as a Springer monograph, in 1991, 1993, and 1997. The frrst three editions were focused on applications. The last was considerably different, by including some chapters with mathematical background material (ordinary differential equations and iterated maps), so as to make the book more self-contained and suitable as a textbook for economics students of dynamical systems. To the same pedagogical purpose, the number of illustrations were expanded. The author also prepared some of the software used in producing the illustrations for use by the readers on the PC, by making the programs interactive and providing them with a user interface. Simulations are essential, when dealing with nonlinear systems, where closed form solutions do not exist. Even theoretical science then becomes experimental. (The software prepared for that book can still be acquired directly from the author at the address tonu. puu@econ. umu. se. ) The present book has been so much changed, that I felt it reasonable to give it a new title. There are two new mathematics chapters (on partial dif- ferential equations and on catastrophe theory), making the mathematical back- ground material fairly complete. There is also an account of the recently emergent method of critical lines and absorbing areas for non-invertible maps added to the chapter on maps.