The aim of this book is to give a fairly complete, yet simple, treatment of the techniques from Functional Analysis used in the modern theory of Partial Differential Equations and illustrate their applications via examples. The book provides an introduction to the theory of Distributions, Sobolev Spaces and Semi groups and the results are applied to the study of weak solutions of elliptic boundary value problems and evolution equations. It also contains an introduction to some techniques in nonlinear analysis and touches upon some of the frontiers of current research in that area. The material in the text is supplemented by four appendices, bibliographic comments at the end of each chapter and several exercises. These exercises are fully solved in a companion volume. This book should be of use both as a textbook and as a source of reference for research workers in the area.
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