Systematically describes the main tasks, methods and results of the dynamics of bodies in contact with a solid surface . The dynamics of a solid body on an absolutely rough surface, as well as on an absolutely smooth horizontal plane with dry or viscous friction of the slip is considered in detail. A number of problems about the movement of the body with a cavity containing liquid on a fixed horizontal surface have been studied. A study of the dynamics of a solid body in the presence of its collisions with an absolutely smooth plane was conducted. For specialists in the field of gyroscopy, solid state dynamics and analytical mechanics, as well as undergraduate and postgraduate students of universities and universities .