The major target of the e-book is to supply a scientific and didactic method of the physics and know-how of free-electron lasers. various figures are used for illustrating the underlying rules and ideas and hyperlinks to different fields of physics are supplied. After an creation to undulator radiation and the low-gain FEL, the one-dimensional idea of the high-gain FEL is constructed in a scientific method. specific emphasis is wear explaining and justifying a number of the assumptions and approximations which are had to receive the differential and crucial equations governing the FEL dynamics. Analytical and numerical ideas are awarded and demanding FEL parameters are outlined, reminiscent of achieve size, FEL bandwidth and saturation energy. some of the most very important good points of a high-gain FEL, the formation of microbunches, is studied at size. the rise of achieve size because of beam strength unfold, house cost forces, and three-d results resembling betatron oscillations and optical diffraction is analyzed. The mechanism of Self-Amplified Spontaneous Emission is defined theoretically and illustrated with a number of experimental effects. a variety of equipment of FEL seeding through coherent exterior radiation are brought, including experimental effects. The world’s first gentle X-ray FEL, the person facility FLASH at DESY, is defined in a few element to provide an influence of the complexity of such an accelerator-based gentle resource. The final bankruptcy is dedicated to the recent tough X-ray FELs which generate tremendous excessive radiation within the Angstrøm regime. The appendices comprise supplementary fabric and extra concerned calculations.