This survey of nonsmooth analysis sets out to prove an inverse function theorem for set-valued maps. The inverse function theorem for the more usual smooth maps plays a very important role in the solution of many problems in pure and applied analysis, and we can expect such an adaptation of this theorem also to be of great value. For example, it can be used to solve convex minimization problems and to prove the Lipschitz behavior of its solutions when the natural parameters vary--a very important problem in marginal theory in economics
