This work is a revised edition of an earlier book by Academician Luikov which was widely used throughout the Soviet Union and the surrounding socialist countries. The presentation is unique in that it not only treats heat conduction problems by the classical methods such as separation of variables, but, in addition, it emphasizes the advantages of the transform method, particularly in obtaining short time solutions of many transient problems. In such cases, the long time solution may be obtained from the classical approach, and by interpolation, a very good estimate is obtained for intermediate times. The text is also noteworthy in that it covers a wide variety of geometrical shapes and treats boundary conditions of constant surface temperature, and constant surface heat flux, as well as the technically important case of a convective boundary condition.The level of the book is advanced undergraduate or graduate. In addition to its value as a textbook, the availability of many technically important results in the form of tables and curves should make the book a valuable asset to the practicing engineers.The scan quality is poor.