AGILE is an Italian Space Agency mission dedicated to the observation of the gamma-ray Universe. The AGILE very innovative instrumentation combines for the first time a gamma-ray imager (sensitive in the energy range 30 MeV - 50 GeV), a hard X-ray imager (sensitive in the range 18-60 keV) together with a Calorimeter (sensitive in the range 300 keV - 100 MeV) and an anticoincidence system. AGILE was successfully launched on April 23, 2007 from the Indian base of Sriharikota and was inserted in an equatorial orbit with a very low particle background. AGILE provides crucial data for the study of Active Galactic Nuclei, Gamma-Ray Bursts, pulsars, unidentified gamma-ray sources, Galactic compact objects, supernova remnants, TeV sources, and fundamental physics by microsecond timing. An optimal angular resolution (reaching 0.1-0.2 degrees in gamma-rays, 1-2 arcminutes in hard X-rays) and very large fields of view (2.5 sr and 1 sr, respectively) are obtained by the use of Silicon detectors integrated in a very compact instrument. The paper describes the AGILE Mission and its space and ground segments.