Symmetries of an action General variation formula Action invariance under finite-dimensional transformations, 1st Noether theorem Gauge invariance and the 2nd Noether theorem, constraints and Noether identities, degrees of freedom Constraints and Noether identities in electrodynamics and gravity Einstein equation solving using perturbation theory Metric disturbances as gauge fields Gauge transformations for metric disturbances, Lorentz gauging, cross-traceless gauging Linearized Riemann tensor, linearized Einstein equations Short-wave approximation, propagation of gravitational waves, gravitational energy-momentum tensor, gravitational emission Spherically symmetric solutions General form of spherically symmetric metric Generalized Birkhoff theorem Spherically symmetric vacuum solution of Einstein equations, Schwarzschield metric and black holes Singularities in the center of the Schwarzschield metric and on its gravitational radius, acceleration of a rest observer Radial falling of massless and massive particles, gravitational red and violet shifts, trajectory classification Formula derivation for shift of the Mercury perihelion Black holes Black hole, horizon of events, singularity, trap surface, cosmic censorship, Hawking theorem “Boldness” theorem for black holes, parameters of stationary black holes; Kerr, Kerr-Newman and Reisner-Nordstrom metrics Space-time of the rotating Kerr black hole, horizon, static limit and ergosphere Celestial mechanics in Kerr geometry, negative energy trajectories, Penrose idea on extracting of energy from rotating black holes Maximally symmetric spaces Algebra of Killing vectors and geometry Homogeneity, isotropy and respective theorems; maximal symmetry and its connection with homogeneity and isotropy Riemann tensor of the maximally symmetric space, constant curvature spaces, conformal flatness, coordinate equivalence Metric of the maximally symmetric space; Lobachevsky, de Sitter and anti-de Sitter spaces Metric of a space with a maximally symmetric subspace Spatially homogeneous and isotropic solutions Einstein equations in Robertson-Walker metric, constraints to be imposed on the matter Friedmann solutions for radiation, dust and cosmological term Galaxy scattering, motion of massless and massive particles in the expanding Universe, cosmological red shift Measurement of distances in the expanding Universe, lens effect, Olbers paradox Elements of cosmology Hot Universe theory, relict radiation Problems of flatness and horizon Inflation as a solution of these problems Scalar field as an inflation generator, inflation theory, full history of the Universe Gravitational instability, Jeans theory; scalar, vectorand tensor modes, its meaning   LITERATURE: A. Lightman, V. Press, R. Price, S. Teukolsky. Collection of problems on GTR and gravity S. Weinberg. Gravity and cosmology Ch. Misner, K. Thorne, G. Wheeler. Gravity (Vol. 2-3) L.D. Landau, E.M. Lifshitz. The theory of field (Vol. 2) A.D. Linde. Physics of elementary particles and inflationary cosmology I.D. Novikov, V.P. Frolov. Physics of black holes