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This volume contains a selection of the lectures given at the Fourth International Workshop on Instabilities and Nonequilibrium Structures in Valparaíso, Chile, in December 1991.§The contents are divided into two parts. Part I includes papers dealing with statistical mechanics, mathematical aspects of dynamical systems and stochastic effects in nonequilibrium systems. Part II is devoted mainly to instabilities and self-organization in extended nonequilibrium systems. The study of partial differential equations by numerical and analytic methods plays a great role here. The most recent developments in this fascinating and rapidly growing area are discussed. §For mathematicians, physicists and engineers interested in dynamical systems, statistical mechanics, and nonequilibrium systems.