The textbook is written in accordance with the current standards of physical specialties of universities and is designed both to support the development of the lecture course, and for independent work. In the presentation of fundamental issues, the traditional methodological approach is used, the novelty of the textbook is determined primarily by the selection of material and the updating of the internal logic of the course. Stronger links of mechanics with other branches of theoretical physics - from atomic physics and plasma physics to solid state physics and cosmology The share of continuous environment mechanics in the course that has become its organic part has been increased due to the transition from the mechanics of material point systems to the mechanics of large number of particle systems (gasodynamics with thermodynamic elements) with access to the continuum phenomenology .. On this basis, the mechanics of ideal and viscous gases and liquids, elastically and irresistibly deformable solids . are presented. The last chapter of the textbook presents an overview of current trends in modern mechanics of complex systems - hereditary mechanics, mesomechanics, fractional differential mechanics, nonlinear dynamics, etc. Despite the attraction of such mathematical means , as functional derivatives, Derivatives of fractional orders , Non-linear , integral and integro-differential equations , The book is written at , level. Available for students of physical and engineering specialties of universities , and can be used in the study of the initial section of the course of theoretical physics.