Abstract
Basic amplification mechanism of free electron laser (FEL) is explained and small signal gain of Compton regime FEL and growth rate of Raman and High gain Compton regime FEL are shown. FELs, which do not use magnetic wiggler, such as Smith-Purcell FEL or Cherenkov FEL are also explained. We also briefly review about startup and slippage which take place in short wavelength FELs using short micro-pulse electron beam.