The course is devoted to a critical analysis of the current state of the science of radiochemistry and the prospects for its development. In the first part (fundamental radiochemistry), such aspects as the kinetics of decay and accumulation of radionuclides are considered, synthesis and properties of new transuranic elements, chemistry of muonium and positronium, chemistry of the ultrafiltered state and diffusion of radionuclides in solids, liquids and gases, radioactive equilibria in natural and reactor radioactive families, isotopic and recoil effects, and also discussed modern methods of separation, concentration and processing of radioactive substances. Considerable attention is paid to the chemistry of hot atoms.