M. Moscow Post . Un-ta, 1989. - 192 s. The manual is the third part of the course "Quantum field theory" (Ch.) 1 "Quantum electrodynamics" -1983 g. , H. 2 Calibration Fields - 1986 . ) and is devoted to the application of methods of modern quantum field theory to solve the problems of interaction of elementary particles of high energies in the presence of external fields . Particular attention is paid to the application of the method of exact solutions of relativistic equations of particle motion in external fields. The following issues are considered: synchrotron radiation, the birth and annihilation of electron-positron pairs in a strong magnetic field ; dynamic nature of the anomalous magnetic moment (AMM) of the electron, which is manifested depending on the AMM of the particle energy and the external field strength ; vacuum effects in non-abel calibration fields.