Spurred by the development of high-current, high-energy relativistic electron beams this books delves into the foundations of a device and geometry independent theoretical treatment of a large collection of interacting and radiating electron bunches. Part I deals with the basics of the radiation emission of a single charged particle, paying particular attention to the effect of radiation reaction and dwelling on the corresponding well-known paradoxes. Part II investigates the collective behaviour of a high-density electron bunch where both discrete and continous beam modelling is explored. Part III treats the application to modern systems while still keeping the treatment as general as possible.