This book reproduces, in a considerably revised and enlarged form, the contents of a course of lectures, delivered by me in Spring 1931 at the invitation of the Seismological Institute of the Academy of Sciences of the U.S.S.R. before the scientific workers of the Institute, and of lectures delivered in 1932 before post-graduate students of the Physico- Mathematical Institute of Mathematics and Mechanics at the University of Leningrad. The lectures were intended for persons acquainted with the principles of the theory of elasticity and were to be devoted to separate fundamental questions the choice of which was largely left to me; I naturally dwelt on subject matter in which I had been working myself.Thus, this book deals only with a few chapters of the theory of elasticity each of which receives fairly complete treatment. I shall not touch here on the subject matter of the book an idea of which may be gained from the list of contents, but I consider it necessary to make the following comments.