Delay ordinary and partial differential equations The book is devoted to linear and nonlinear ordinary and partial differential equations with constant and variable delay. It considers qualitative features of delay differential equations and formulates typical problem statements. Exact approximate analytical and numerical methods for solving such equations are described including the method of steps methods of integral transformations method of regular expansion in a small parameter method of matched asymptotic expansions iteration type methods Adomian decomposition method collocation method Galerkin type projection methods Euler and Runge Kutta methods shooting method method of lines finite difference methods for PDEs methods of generalized and functional separation of variables method of functional constraints method of generating equations and more. The presentation of the theoretical material is accompanied by examples of the practical application of methods to obtain the desired solutions. Exact solutions are constructed for many nonlinear delay reaction diffusion and wave type PDEs that depend on one or more arbitrary functions. A review is given of the most common mathematical models with delay used in population theory biology medicine economics and other applications. Delay Ordinary and Partial Differential Equations contains much new material previously unpublished in monographs. It is intended for a broad audience of scientists university professors and graduate and postgraduate students specializing in applied and computational mathematics mathematical physics mechanics control theory biology medicine chemical technology ecology economics and other disciplines. Individual sections of the book and examples are suitable for lecture courses on applied mathematics mathematical physics and differential equations for delivering special courses and for practical training