The Cherenkov Telescope Array Observatory (CTAO) is a multinational project to build a new generation of ground-based gamma-ray instruments in the energy range extending from some tens of GeV to about 300 TeV. It is proposed as an open observatory and will consist of two arrays of imaging atmospheric Cherenkov telescopes, a first array in the Northern Hemisphere, on the Spanish island of La Palma, with emphasis on the study of extragalactic objects at the lowest possible energies, and a second array in the Southern Hemisphere, in the Atacama Desert in Chile, which is to cover the full energy range and concentrate on galactic sources. The physics program of the CTAO goes beyond high-energy astrophysics into cosmology and fundamental physics.