The textbook is devoted to the presentation of the foundations of the theory of transport processes - diffusion, heat transfer, hydrodynamic currents. All phenomena are considered within the framework of approximation of continuum mechanics. The main attention is paid to the analysis of the physical side of the phenomena under study, as well as to the principal ideas and methods of solving transport equations. In contrast to standard textbooks on this topic, in addition to the classical sections of transfer theory, important, for the modern practical application of transfer theory methods, sections are considered. diffusion through potential barrier, heat waves in chemical reaction media, rheology of viscoelastic media, colloids and polymers. The manual is intended for students of 2-4 courses of the Faculty of Mathematics and Mechanics . It will be useful for students of physical and chemical faculties .