The construction and selection of realistic cosmological and astrophysical models in various modified (non-Einstein) theories of gravity with the aim of obtaining a good correspondence between theoretical results and modern observational data. The problem of dark energy and dark matter. Formation of the structure of the niverse. The study of the global properties of the cosmological dynamics of the theory of gravitation with a non-minimal kinetic coupling. Investigation of cosmological perturbations (tensor, vector, and scalar modes) in the scalar-tensor theory of gravitation.