The book is devoted to a detailed analysis of the mathematical foundations of elasticity theory. At the modern level of mathematical rigor, for the first time, three-dimensional problems of statics, harmonic oscillations and the general dynamics of the linear theory of elasticity, thermoelasticity and moment elasticity . are considered with equal completeness. The method of multidimensional singular integral equations and singular potentials, developed in the book, investigated general problems of theory and obtained representations of solutions in rows and quadratures that allow for effective implementation on computers ..