The Fermi Gamma-Ray Space Telescope is a satellite-based observatory that studies the gamma-ray sky in a wide energy range from a few keV to more than 300 GeV, allowing the investigation of many fields of gamma ray astrophysics. Fermi will open a new and important window on a wide variety of phenomena, including active galactic nuclei and gamma-ray bursts, the origin of cosmic rays and supernova remnants, pulsars and gamma-ray binaries, solar system objects, searches for hypothetical new phenomena such as supersymmetric dark matter annihilations. Fermi was launched in June 2008 from Kennedy Space Flight Centre (NASA). The primary instrument is the Large Area Telescope (LAT), which measures gamma-ray flux and spectra from 20 MeV to > 300 GeV and is a successor to the highly successful EGRET experiment on CGRO and the Italian space Agency Small Mission AGILE. The LAT has better angular resolution, greater effective area, wider field of view and broader energy coverage with respect to EGRET. In this talk a review of the Fermi physics and the first three months results will be presented.