This book is especially concerned with fundamental theoretical and experimental aspects of relativistic beam physics, recoil, and cooling phenomena in atomic and ion beams and traps, with emphasis on coherence and collective effects. The central theme is the physics of atomic laser and free electron laser, and the development of a bridge between them through the mechanism of the so-called recoil induced gain mechanism. The links between relativistic beam physics and atomic laser physics are explored. This book is targeted at an audience of non-specialists or specialists in only one of the fiel.