This book is devoted to the theory of infinite-order linear and nonlinear differential operators with several real arguments and their applications to problems of partial differential equations and numerical analysis.Part I develops the theory of pseudodifferential operators with real analytic symbols, the local representatives of which are linear differential operators of infinite order acting in the spaces of basic and generalized functions based on the duality of the spaces of real analytic functions and functionals. Applications to a variety of problems of PDEs and numerical analysis are given. Part II is devoted to the theory of Sobolev-Orlicz spaces of infinite order and the solvability of nonlinear partial differential equations with arbitrary nonlinearities.Contents:PreliminariesPseudo-Differential Operators with Real Analytic SymbolsApplications to Pseudo-Differential EquationsApproximation MethodsA Mollification Method for Ill-Posed ProblemsNontriviality of Sobolev-Orlicz Spaces of Infinite OrderSome Properties of Sobolev-Orlicz Spaces of Infinite OrderElliptic Equations of Infinite Order with Arbitrary NonlinearitiesReadership: Mathematicians, engineers and physicists.Key Features:Describes the problems and methods in nonequilibrium statistical mechanics of condensed matter