About a dozen of the most important cosmological problems posed by modern astronomical observations will be discussed in the report. The solution of these problems is of a paramount importance for the whole fundamental physics. The ongoing theoretical studies, as well as possible directions for the future work, will also be discussed. We also consider the modern high-precision telescopes, or rather, the detectors of all forms of radiation coming from space and the prospects for their further development. Traditionally, Russia occupied and still occupies a leading position not only in theoretical works, but also in space observations. It is necessary not only to maintain but to develop and strengthen such provision.