The Alpha Magnetic Spectrometer (AMS) is a particle physics detector designed to measure charged cosmic rays spectra up to TV region, with high energy photon detection capability up to few hundred GeV. With the large acceptance, the long duration (3 years) and the state of the art particle identification techniques, AMS will provide the most sensitive search for the existence of antimatter nuclei and for the origin of dark matter. The detector is being constructed with an eight layers Silicon Tracker inside a large superconducting magnet, providing a 0.8 Tm^2 bending power and an acceptance of 0.5 m^2sr. A Transition Radiation Detector and a 3D Electromagnetic Calorimeter allow for electron, positron and photon identification, while independent velocity measurements are performed by a Time of Flight scintillating system ans a Ring Imaging Cherenkov detector. The overall construction is due to be completed by 2008.