The monograph provides a detailed and comprehensive presentation of the rich and beautiful theory of unilateral variational analysis in infinite dimensions. It is divided into two volumes named Part I and Part II. Starting with the convergence of sets and the semilimits and semicontinuities of multimappings, the first volume develops the theories of tangent cones, of subdifferentials, of convexity and duality in locally convex spaces, of extended mean value inequalities in absence of differentiability, of metric regularity, of constrained optimization problems.The second volume is devoted to special classes of non-smooth functions and sets. It expands the theory of subsmooth functions and sets, of semiconvex functions and multimappings, of primal lower regular functions, of singularities of non-smooth mappings, of prox-regular functions and sets in general spaces, of differentiability of projection mapping and others for prox-regular sets. Both volumes I and II contain, for each chapter, extensive comments covering related developments and historical comments.Connected area fields of the material are: optimization, optimal control, variational inequalities, differential inclusions, mechanics, economics. The book is intended for PhD students, researchers, and practitioners using unilateral variational analysis tools.Key FeaturesThe book should have great interest for researchers in mathematical analysis, in optimization, in optimal control, in mathematical economics, etc; for postgraduate and graduate students in the above fields; many exercises are included for these studentsSeveral new fundamental topics of variational analysis developed during the last ten years are extensively developedThe manuscript contains several chapters included in no other previous book. It presents for the first time in infinite dimensions and in complete forms, the following chapters: Sequential Mean Value Inequalities; Subsmooth Sets and Functions; Semiconvex Functions; Subdifferential Determination; Lower Regular Functions; Prox-Regular Sets in Hilbert Spaces; Prox-Regular Sets in Banach Spaces; and some others

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