Gamma rays, electrons and positrons up to 3 TeV with the Fermi Gamma-ray Space Telescope

The Fermi Gamma-ray Space Telescope (formerly known as Gamma-ray Large Area Space Telescope, GLAST) was successfully launched on June 11 2008. Its main instrument is the Large Area Telescope (LAT), which detects gamma rays from 20 MeV to more than 300 GeV. It is a pair-conversion telescope with 16 identical towers (tracker and calorimeter), covered by an anti-coincidence detector to reject charged particles. The calorimeter is a hodoscopic array of CsI(Tl) crystals, arranged in 8 alternating orthogonal layers, with a total thickness of 8.6 radiation lengths. In this paper we will present the performance of the LAT, with special attention to the calorimeter, which provides a good energy measurement up to 3 TeV. We will also review some of its scientific results after 4 years of operation, focusing on measurements which extend up to very high energy, such as the spectrum of the extragalactic diffuse emission, the spectrum of cosmic electrons and the positron fraction.