This book contains a systematic treatment of the basic principles of free elec­ tron laser (FEL) physics. It is primarily intended for physicists specializing in FEL physics and related fields: laser physics, microwave electronics, particle accelerator physics, etc. At the same time it might be useful for those who use the FEL as a research or industrial tool. The treatment requires that the reader has a knowledge of classical me­ chanics and electrodynamics. It is assumed that the reader is familiar with the kinetic theory of charged particle beams, in particular the Vlasov equa­ tion. All the results presented here are derived from "first principles", and all steps involving physical principles are given. To preserve a self-consistent style, we place the derivation of auxiliary results in appendices. Theoretical study is performed with an extensive use of similarity tech­ niques, so the results obtained are simultaneously highly general and com­ pletely specified. The use of similarity techniques involves a particular way of thinking and leads to a deeper insight into FEL physics. We use a synthetic approach to present the material: some simple models are studied first, and more complicated ones are introduced gradually. We start with the one-dimensional theory of the FEL amplifier and FEL oscilla­ tor. Then we move on the analysis of diffraction effects and waveguide effects. Finally, we introduce the reader to the part of FEL theory dealing with the start-up from shot noise in the electron beam.