The present paper contains a systematic exposure of basic principles o
f free electron laser physics. FEL models are discussed wherein space
charge fields, energy spread of the electrons in the beam and diffract
ion effects are taken into account. We present a detailed study of the
one-dimensional theory of a FEL amplifier, FEL oscillator and FEL osc
illator with multicomponent undulator. We present also an introduction
to the analysis of the diffraction effects using the FEL amplifier mo
del. When exposing linear theory we use analytical techniques and the
investigation of nonlinear modes in the operation of FEL devices is pe
rformed using the results of numerical simulations. The results of the
linear theory serve as a primary standard to check the accuracy of nu
merical simulations. We perform a thorough analysis of the saturation
effects in the FEL devices and of the methods to increase the FEL effi
ciency. A theoretical study is performed with a wide use of similarity
techniques, so the obtained results are simultaneously of high degree
of generality and completely specified. Numerous universal graphs ill
ustrating various modes of the FEL operation together with the reduced
design formulae can help the reader to find FEL characteristics using
simple dimensional analysis only. It may be useful also for FEL desig
ners, especially at the design stage of an experiment.