This course has two themes, which are closely related: the generation of electromagnetic radiation by charged particles and the relativistic (covariant) theory of electromagnetic fields. Starting from maxwell’s equations, the course lays the foundation for the theoretical description of fundamental processes in plasma and beam physics and provides a solid classical basis for quantum theories of the interaction between light and matter. Topics treated range from the fundamental problem of radiation reaction - the oldest unsolved problem in physics - to the generation of brilliant X-ray beams in accelerator-based light sources, extremely important tools in life sciences and materials science.