Construction principles of the theory of gravity Dicke systematization Principle of equivalence. Its experimental check Examples: action for a particle in the gravitational field and the Newtonian limit Classical tests of GRT: deflection of light rays by the Sun the delay of radio-signals the shift of the Mercury perihelion oscillations of the Moon orbit pulsar in the double system Construction rules for gravitational physics following from the Principle of equivalence Tensorial analysis foundation Notion of a manifold Tensors, metric, covariant derivative Christoffel symbols, its direct derivation and properties Basic formulae Curvature tensor and its properties Inability of its construction from the 1st derivatives Its uniqueness Riemannian tensor, its symmetries Ricci tensor, Einstein tensor and Weil tensor Scalar invariants Parallel transport, carrying around a closed contour Commutation of covariant derivatives Theorems concerning Riemannian and Weil tensors Bianchi identities Geodesics and its equation, affine parameters Operator notation, commutator, curvature operator Geodesic deviation equation Lie and Fermi-Walker translations, simultaneity Physical necessity for translation procedures Lie derivative, its properties and notation Fermi-Walker translation, gyroscope translation and Thomas precession Comparison of these translations Notion of event simultaneity, clock synchronization condition Gaussian normal coordinate system Smooth curve congruence, degrees of freedom of coordinate systems, vector fields and congruences Killing vectors and its properties Integration in curved spaces, Stocks theorem, metric on the hypersurface of simultaneity Isometry and Killing vector, equation and properties Killing vector decomposition in a point, maximal set of Killing vectors Killing vectors and conservation laws Exterior curvature Induced metric and exterior curvature of a hypersurface Symmetry of the exterior curvature, connection with Lie derivative of the projecting operator Exterior curvature of the surface of simultaneity Gauss-Codazzi equations Einstein action General structure of the gravitational action Variational formulae Variation of the gravitational action Variation problems on a boundary, surface term and its variation Momentum-energy tensor, Einstein equation in the presence of matter   LITERATURE: A. Lightman, V. Press, R. Price, S. Teukolsky. Collection of problems on GTR and gravity K. Will. Theory and experiment in gravitational physics S. Weinberg. Gravity and cosmology Ch. Misner, K. Thorne, G. Wheeler. Gravity (Vol. 1-2)