This book is the first part of the textbook "Gyroscopic Systems." The book outlines the applied theory of gyroscopes, one-, two- and three-axis gyroscopic stabilizers, principles and methods of gyroscopic stabilization of spacecraft; much attention is paid to the physical processes taking place at the same time. The 2nd edition (1st - 1971) introduced new sections on the maintenance of standard schemes for the construction of devices, systems and their elements.