This book provides a basic introductory course in partial differential equations, in which theory and applications are interrelated and developed side by side in a systematic manner. It has been attempted to make the presentation of the various topics comprehensive, rigorous and yet simple. It is designed primarily to serve as a textbook for postgraduate students pursuing courses in mathematics, applied mathematics, physics, engineering and technology. It provides the students with various well-known mathematical techniques such as the characteristic method, separation of variables method, integral transform techniques and Green's functions approach to solve a number of mathematical and physical problems. This book is enriched with worked-out examples and supplemented with a variety of exercises at the end of each chapter. Students appearing for competitive examinations like NET, GATE and the professionals working in RD organizations would also find this text useful.