Abstract: The giant radio galaxy M 87 was observed at GeV/TeV γ-ray energies with the H.E.S.S. (High Energy Stereoscopic System) Cherenkov telescopes in the years 2003-2006. The observations confirm M 87 as the first extragalactic TeV γ-ray source not of the blazar type (first indications of a signal were reported by the HEGRA collaboration earlier). The TeV γ-ray flux from M 87 as measured with H.E.S.S. was found to be variable on time-scales of years and surprisingly also of days which strongly constrains the size of the emission region. The results (position, energy spectrum and light curve) as well as theoretical interpretations will be presented