The goal of this publication is to provide basic tools of differential topology to study systems of nonlinear equations, and to apply them to the analysis of general equilibrium models with complete and incomplete markets. The main content of general equilibrium analysis is to study existence, (local) uniqueness and efficiency of equilibria. To study existence Differential Topology and General Equilibrium with Complete and Incomplete Markets combines two features. First, order conditions (of agents' maximization problems) and market clearing conditions, instead of aggregate excess demand functions. Then the application to that "extended system" of a homotopy argument, which is stated and proved in relatively elementary manner. Local uniqueness and smoothdependence of the endogenous variables from the exogenous ones are studied using a version of a so called parametric transversality theorem. In a standard general equilibrium model, all equilibria are efficient, but that is not the...

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