Moduli Spaces of Vector Bundles over a Real Curve: $\mathbb Z/2$-Betti Numbers Moduli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi-stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah-Bott's Yang-Mills over a Riemann Surface'' to compute $\mathbb Z/2$-Betti numbers of these spaces. Keywords:cohomology of moduli spaces, holomorphic vector bundlesCategories:32L05, 14P25