Revolutionary development of astrophysics in the second half of the twentieth century. Key opening (cosmic microwave background, cosmic masers, radio lines, quasars, radio galaxies as a manifestation of activity of galactic nuclei, radio pulsars, X-ray pulsars and other compact sources of X-rays, gamma-ray bursts, gravitational lenses and microlenses, the sources of gamma-ray bursts) Radio pulsars The main observational properties. The pulsar in the Crab Nebula. Accidental opening. Theoretical predictions. Electromagnetic braking mechanism Determination of the evolution of neutron star with magnetodipole radiation.Characteristic time of life. Derivation of formula for magnetodipole loss from qualitative consideration. Radio pulsars magnetosphere Model of a unipolar inductor. Current loss of neutron stars. Magnetosphere of black holes Pulsar 1913 +16 in the binary system The first radio pulsar in binary system. A unique gravity lab. Doppler effect and its use in astronomy (determination of orbital elements, the mass function (with derivation)). Post-Newtonian corrections Deflection of light. Gravitational red shift. Motion of the perihelion (periastron). Shapiro delay. Gravitational radiation Power of gravitational radiation. Absence of dipole gravitational radiation. Energy density of gravitational field. Derivation of formula for the gravitational loss. Measurement of lengths in astrophysics Radiolocation. Parallax. Cepheids. Supernovae. Search for black holes The black holes of solar mass. Supermassive black holes in galactic nuclei Plasma frequency Permittivity of medium. Derivation of expression for plasma frequency The main observational ranges - line and continuous radiation Radio astronomy. Optical astronomy. X-ray astronomy. Gamma-astronomy. Gamma-ray bursts The first observations, interpretation as neutron stars. Contradiction isotropy - heterogeneity. Afterglow - cosmological nature of gamma-ray bursts. Criterion LogN - LogS. Introduction to the general theory of relativity Limitation of the classical theory of gravitation. Group properties for the rotation. Invariance of equations of electrodynamics under the Lorentz transformation. Tensors in physics. Metric tensor. Energy-momentum tensor. Curvature. Geodesics. The triangles and circles. Gaussian curvature. Einstein's equations Heuristic consideration. Gravity as curvature. The limiting process to the nonrelativistic case. New (old forgotten?) ideas in the mathematical physics in the last of XX century Fractality, chaos and catastrophe. Topology Orientable and nonorientable surfaces. Poincare indexes. Eulerian characteristic. Nematic crystals - an example of the topology of the projective plane. Opportunity of nontrivial topological structure of the universe. Fractals Hausdorff dimension. Fractality of sunspots. Aggregations, aerogels. Diffusion in fractal space. Phase plane Mappings. Feigenbaum process. The theory of Kolmogorov-Arnold-Moser (KAM) Arnold diffusion. Saturn rings. Astrophysical examples (asteroids, Kirkwood ports, instability of the orbits of satellites of the Earth and the Moon). Theory of groups The concept of the group. Cyclic group. Commutative Groups Isomorphism Subgroups Direct product of groups. Cosets Lagrange's theorem. Inner automorphisms Normal subgroups. Commutant Solvable group. Homomorphism Natural homomorphism. Groups of permutations Theorem of the unsolvability of the group of permutations for n> 4. Abel's Theorem   LITERATURE William J. Kaufman The Cosmic Frontiers of General Relativity A.M.Cherepashchuk, A.D. Chernin. The Universe, Life, and Black Holes. Karlov N.V., Kirichenko N.A. Oscillations, Waves, Structures. Alekseev V.B. Abel's theorem in problems and solutions.