The analytical review of selected works (hereinafter referred to as the analytical review or review) presents the results of theoretical research on the development of a model for the formation of planetary systems, including their satellites, for solar-type stars – a model of gas and dust rings. This model is based on the origin and development of large-scale gravitational instabilities (gas and dust rings) in the protoplanetary disks of stars, and subsequently in protosatellite disks. The analytical review presents the results of comparing the main theories and models of the formation of planetary systems of solar-type stars with the data of astrophysical observations of protoplanetary disks. It is shown that the data of astrophysical observations are most fully substantiated in the model of gas-dust rings. In this model, at the stage of formation of protoplanetary rings, a theoretical forecast is given based on astrophysical observations of the evolution of the structures of gas-dust rings for a number of protoplanetary disks of stars. Proposals have been formulated for the further development of numerical algorithms for the evolution of protoplanetary disks of solar-type stars, including all stages of evolution, including the formation of protoplanets. The review is dedicated to the memory of Corresponding Member of the Russian Academy of Sciences Alexei Valerievich Zabrodin (14.12.1933 – 28.09.2008) in connection with the ninetieth anniversary of his birth.