In a free-electron laser (FEL) the lasing medium is a high-energy electron beam flying with relativistic speed through a periodic magnetic field. The interaction between the spontaneous synchrotron radiation that is produced and the electrons in the beam induces a periodic micro-bunching of the electrons, greatly increasing the intensity of radiation produced at a particular resonant wavelength, the so called Self Amplified Spontaneous Emission (SASE) regime. The FEL concept can be adapted to produce radiation wavelengths from millimetres to Angstroms, and can in principle produce hard x-ray beams with unprecedented peak brightness, exceeding that of the brightest synchrotron source by ten orders of magnitude or more.
In this talk the basic physics of the FEL concept will be introduced and the wide range of applicability will be illustrated. A particular emphasis will be devoted to the recent promising results obtained at SPARC. New techniques to produce ultra-fast radiation pulses based on original schemes developed at LNF will be also discussed.