This text reflects the authors' unique approach to the study of the basic types of partial differential equations of mathematical physics. The system­ atic presentation of the material offers the reader a natural entree to the subject. Each of the basic types of equations which are to be studied is motivated by its physical origins. The derivation of an equation from the physics to its final mathematical structure is very instructive to the student.The authors have gone to great length to make clear the meaning of a solution to an initial value or boundary-value problem. Various methods of solving such problems are treated in great detail, as are the questions of existence and uniqueness of solutions. Thus, the student gains an apprecia­ tion of the theoretical foundations of the subject and simultaneously acquires the manipulative skills for solving such problems.The exercises which accompany each chapter have been selected to test the student’s ability both to formulate the correct mathematical statement of the problem and to apply the appropriate method for its solution. The applications treated by the authors are non-trivial and are completely worked out in detail.The present volume covers the two dimensional class of partial differential equations of mathematical physics and is well suited as a basic text for both the undergraduate and graduate level at the university. The second volume will cover the three dimensional counterparts of the present volume and contain an additional chapter on the special functions which arise in mathe­ matical physics.