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

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