Very High Energy astronomy from H.E.S.S. to CTA. Opening of a new astronomical window on the non-thermal Universe

The last ten years saw the emergence of Imaging Atmospheric Cherenkov Telescopes as a mature and efficient technique for the study of the Very High Energy Universe, leading to the successful opening, mainly by the HESS experiment, of our understanding of the non-thermal Universe. This Habilitation thesis summaries ten years of research in Very High Energy gamma-ray astronomy with HESS and CTA. In the first part, instrumental aspects such as the experiment conception, its calibration, the reconstruction of the events and the data analysis are presented. The second parts draws a panorama of the main discoveries in the domain. (author)