A review of the literature on the radiation reaction force on a charged particle shows that the expression given for this force obtained by Lorentz, Abraham, and Dirac is in physically reasonable agreement with the radiation of energy, momentum, and angular momentum, and is successfully used in investigating the motion of particles in a field. A selection of physical solutions by the methods presented herein guarantees that the conservation laws are satisfied. In the first approximation, which is the only one utilized in the majority of physical situations, radiation damping does not depend on assumptions concerning the structure of the charge of the particle. A theory is presented of the losses of energy, momentum and angular momentum by a system of charged particles in the course of their moving together taking into account the external field, the radiation damping forces, and the retarded Lienard-Wiechert forces. Formulas are given for the spectral and angular distribution of the radiation from a system of particles. The concept of a center of a system of events with relativistic particles is utilized in constructing a system of equations for finding the angular momenta of the electromagnetic waves radiated by particles of the system. The angular distribution and the total intensity of the radiation from a system of particles at an arbitrary instant of time is obtained. Using the example of the joint synchrotron radiation from two particles the consistency of all three approaches to the radiation from a system of particles is demonstrated.