In this book, an attempt to augment the physical representations about some phenomena of the quantum electrodynamics in relation to medical physics is made. First of all, the physical theory of an electromagnetic radiation quantum is developed. The Schrodingers equation for a quantum is found and solved. The quantum length, how it is radiated, what the role of a vacuum in these processes, etc. are shown. The explanation of the quark confinement reason (impossibility to leave a hadron by a quark) is given. With the help of the Feynmans diagram method, some physical processes playing an important role in medical physics are analysed in detail: annihilation of the electrons and positrons in photons, breaking of the electrons in an electric field of a nucleus, changing of the quantum polarisation direction at the interaction site with molecules, etc. The use of Feynmans diagram method makes the loss of some physical phenomena accompanying a researched physical process possible, in particular the Doppler effect. On the basis of the quantum electrodynamics, the modern methods of diagnostics are investigated: a positron-emission tomography and a magneto-resonant tomography. Their developmental processes are also discussed. This book will be useful to students and scientists whose interests lay in the fields of quantum electrodynamics and medical physics.