The book establishes links between regularity and derivative concepts of nonsmooth analysis and studies of solution methods and stability for optimization, complementarity and equilibrium problems. In developingnecessary tools, it presents, in particular: an extended analysis of Lipschitz functions and the calculus of their generalized derivatives, including regularity, successive approximation and implicit functions formultivalued mappings; a unified theory of Lipschitzian critical points in optimization and other variational problems, with relations to reformulations by penalty, barrier and NCP functions; an analysis ofgeneralized Newton methods based on linear and nonlinear approximations; the interpretation of hypotheses, generalized derivatives and solution methods in terms of original data and quadratic approximations; a richcollection of instructive examples and exercises. /LIST Audience: Researchers, graduate students and practitioners in various fields of applied mathematics, engineering, OR and economics. Also university teachers andadvanced students who wish to get insights into problems, future directions and recent developments.