H.E.S.S.--the high energy stereoscopic system--is a new system of large imaging atmospheric Cherenkov telescopes, with about 100 m 2 mirror area for each of four telescopes, and photomultiplier cameras with a large field of view (5°) and small pixels (0.16°). The dish and reflector are designed to provide good imaging properties over the full field of view, combined with mechanical stability. The paper describes the design criteria and specifications of the system, and the individual components--dish, mirrors, and Winston cones--as well as their characteristics. The optical performance of the telescope as a whole is the subject of a companion paper.