The monograph is devoted to quantum electrodynamics, t. e. Relativistic theory of motion and interaction of electrons, positrons and photons, and partly c-mesons Considerable attention is paid not only to the systematic presentation of general questions of the theory ,. but also detailed calculations of individual specific effects (interaction of photons with electrons , Birth and annihilation of electrons and positrons , polarization of electron-positron vacuum, Shift in atomic electron levels, positronium, Mesoatoms and others. ). Wherever possible, a single mathematical method is used (Fourier transform, operator division, operator series decomposition, and t.) d. ), which is not difficult to master, having at its disposal a minimum of additional literature on quantum mechanics and equations of mathematical physics The mathematical apparatus developed in the monograph makes it relatively easy to lay out a number of sections related to quantum electrodynamics, for example, the theory of neutrinos with a oriented spin (this theory is of great importance in connection with the discovery of the non-preservation of parity), the theory of attenuation, etc. The monograph is designed for researchers, teachers, graduate students and senior students - physicists and mathematicians interested in modern quantum field theory.