  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.
