2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77748In this paper, the first of a series of three, we classify holomorphic principal G-bundles over an elliptic curve, where G is a reductive group. We also study the local and global properties of the moduli space of semistable G-bundles. We identify canonical representatives for each S-equivalence class of semistable G-bundles, and study their automorphism groups.68 pages, AMS-TeX, amsppt styleAlgebraic GeometryHigh Energy Physics - Theorytext