Abstarct: Free electron laser has a high ability to produce coherent electromagnetic waves with high energy and different wavelengths. One of the advantages of this laser is that it can be adjusted in a wide range of power and different wavelength. The basis of this laser is to convert the kinetic energy of the electron into an electromagnetic wave. This conversion takes place in the presence of an alternating magnetic field produced by a device called an undulator. This alternating field causes the oscillation of relativistic electrons. The synchrotron motion of the electron causes the bremsstrahlung radiation to produce photons. This radiation is incoherent and spontaneous at first but, it returns to electrons after several rounds and collisions with the resonator and categorizes them. Electrons are emitted at the same time as the resonator radiation field, and the electron beam exchanges this kinetic energy to the common radiation field under appropriate resonance conditions. Now the coherent radiation produced passes through the resonator with partial reflection in the form of laser light.In order for this mechanism to be performed more powerfully, the field inside the undulator must be strengthened. The intensity of the field depends on the physical characteristics of the undulator, such as the magnets that make up it, and the distance between the two rows of magnets, wich is called the gap, which is in this thesis has been reviewed. This is the basis of the work of the free electron laser and the important role of the undulator in it. The components of this laser are accelerator, undulator or wiggler and resonator.