2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225572We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of real or quaternionic connections, some of the basic topological invariants of these spaces are calculated.28 pages; revised version; minor correctionsAlgebraic Geometry14D20 (Primary); 14P20, 55R35 (Secondary)text