Selected Problems of Classical and Modern Celestial Mechanics and Stellar Dynamics: I-Classical Results

A review is given, in the modern context of applications, of the major important scientific results obtained by scientists and graduates of St. Petersburg State University in the field of celestial mechanics and stellar dynamics. The following topics are discussed: the Antonov laws of stellar dynamics, Abalakin-Batrakov libration points, Kholshevnikov metrics, Agekyan-Anosova homological region, Orlov metastable triple systems, Ogorodnikoff-Milne models, Ossipkov-Merritt models, estimation and calculation of the MOID parameter, photogravitational celestial mechanics and solar sail, problems of asteroid-comet hazard, dust complexes in the Solar System, rotational dynamics of planetary satellites, circumbinary dynamics, and methods for the discovery and determination of orbits of exoplanets. The first part of the review presents the classical results.