The book presents the classical and quantum theory of the motion and radiation of relativistic electrons. A number of topical issues are considered, for example, the exact solution of some radiation problems in classical electrodynamics, the study of the classical relativistic Dirac-Lorentz equation taking into account the strength of radiation friction, etc. All this finds, especially recently, a great practical application not only for the description of microprocessors, but also when considering the movement of the ultrarelativistic electron along trajectories with a macroscopic radius of curvature (for example, synchrotron radiation). A large place is given to the analysis of such problems with the help of relativistic quantum equations, since, without taking into account quantum effects, it was impossible to design and build modern electronic cyclic accelerators and storage units.