From the analog of Newton's law, Maggi's equations are deduced which are the most convenient equations of the nonholonomic mechanics. From Maggi's equations the most useful forms of equations of motion of nonholonomic systems are obtained. The connection between Maggi's equations and the Suslov - Jourdain principle is considered. The notion of ideal nonholonomic constraints is discussed. In studying nonholonomic systems the approach, applied in Chapter I to analysis of the motion of holonomic systems, is employed. The role of of Chetaev's type constraints for the development of nonholonomic mechanics is considered. For the solution of a number of nonholonomic problems, the different methods are applied.