The Free Electron Laser triggers, for many people, wild fantasies on large scale applications. However, Free Electron Lasers are not so much direct devices for various applications, but form an interesting subject within fundamental physics. The interplay between electric magnetic and the photon field have an intrinsic beauty and are deeply rooted in the fundamental understanding of nature. In this volume, edited by three major initiators in the field and containing contributions from experts belonging to the most advanced groups working on the subject, a first, comprehensive account of the Free Electron Laser is given. Chapters include both complete classical and quantum mechanical descriptions. Various types of experiments with intrinsic strong points and weaknesses are described while attention is also given to state-of-the-art experiments. This book is not intended as a catalogue of on-going experiments. It is the first large scale reference source on which all further publications on Free Electron Lasers will be based. It will therefore be indispensable for theorists and experimentalists interested in the fundamental aspects of these types of lasers.