THE PRESENT book is based on the practical work with equations of mathematical physics done in the Physics Faculty and the external section of Moscow State University. The problems set forth were used in the course "Equations of Mathematical Physics" by A. N. Tikhonov and A. A. Samarskii, and in "A Collection of Problems on Mathematical Physics" by B. M. Budak. However, in compiling the present work the range of problems examined has been considerably enlarged and the number of problems sev­eral times increased. Much attention has been given to problems on the derivation of equations and boundary conditions. A con­siderable number of problems are given with detailed instructions and solutions. Other problems of similar character are given only with the answers. The chapters are divided into paragraphs accord­ ing to the method of solution. This has been done in order to give students the opportunity, by means of independent work, of gain­ ing elementary technical skill in solving problems in the principal classes of the equations of mathematical physics.Therefore this book of problems does not claim to include allmethods used in mathematical physics. For example, the opera­tional method, variational and differential methods and the appli­cation of integral equations are not considered.It is hoped, however, that this book will be useful not only to students but also to engineers and workers in research institutions.