This book presents a systematic, detailed development of approaches to construct ¿ uniformly convergent finite difference schemes for wide classes of singularly perturbed boundary value problems. The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. Containing material published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter.