This textbook is addressed to the needs of applied mathematicians, physicists, engineers etc., who are interested in studying the problems of mathematical physics in general and their approximate solutions on computer in particular. Almost all basic results of the theory of distributions are contained in the book. It contains almost all topics of Sobolev spaces which are essential for the study of elliptic boundary value problems and their finite element analysis. Additional topics have been included along with many interesting examples. Hence it can be read as an introduction to advanced treatises on distributions.