H.E.S.S. is an experiment for ground based GeV/TeV gamma ray astronomy of the new generation. It consists of four large Cherenkov telescopes operating in stereoscopic observation mode. Its construction in Namibia was completed at the end of 2003. Already during the installation phase, exciting results have been achieved, and after completion several discoveries have been made. Some of the results and discoveries are reported, such as the first image of a shell-type supernova remnant resolved at arc minute scale (RXJ 1713 – 3946), the discovery of the unique binary pulsar system PSR B1259 – 63 and of a yet-unidentified source in the same field of view (HESS J1303 – 631), and the observation of the galactic centre region. Amongst the extragalactic sources, the blazers Mkn 421 and PKS 2155 – 304 have also been detected.