Gravitational waves are emitted from a variety of astrophysical and cosmological sources. Study of low frequency waves, emitted for example by coalescing massive black holes, by EMRIs or by the galactic or stochastic background, requires a space based detector. The LISA (Laser Interferometer Space Antenna) project is based on 3 satellites, separated by 5 million kilometers, which exchange laser beams, forming several interferometers. An understanding of this complex project requires the development of simulation softwares such as LISACode (this thesis). It is a new scientific simulator for LISA. Its ambition is to achieve a degree of sophistication allowing to map, as closely as possible, the impact of the different sub-systems on the measu...