In the paper topical problems of the structure and evolution of the universe are analyzed. The consequencies of different velacities of the evolution of stars of different mass for the whole evolution of galaxies are shown. The question of the age of galaxies is studied in detail. Basing on the occurrence of the oldest known stars in all types of galaxies it is concluded that all galaxies are of the same age and rised in a single process 12—15 billion years ago. This conclusion, together with the confirmed one-way change of chemical composition of the universe and with further new evidence, unambiguously refutes both the conception of the stationary universe and the cyclic character of the evolution of cosmical objects. The discovery of relict background radiation with its high degree of isotropy confirms correctness of Fridman’s models with the hot beginning of the evolution of the universe. In the end open problems of modern cosmology are presented.