The textbook consists of two parts: tensor calculus and continuum mechanics. The first part deals with the algebra of tensors on linear spaces and spaces with quadratic metrics. Basic concepts of invariants . Tensor analysis is constructed in arbitrary point Euclidean spaces with partial use of Riemannian space theory. In the second part, on the basis of the apparatus of tensor analysis in arbitrary curvilinear coordinate systems, the main sections of continuum mechanics are presented: the theory of deformations and stresses, thermodynamics, closed systems and the formulation of corresponding initial boundary problems. Linearized models are justified . Examples of classical models of continuous media. are given. For university students studying continuum mechanics and its sections, as well as graduate students of the relevant profile.