(This talk is aimed at graduate students and postdocs.)  In "The Yang-Mills equations over Riemann surfaces," Atiyah and Bott studied the Yang-Mills functional over a Riemann surface from the point of view of Morse theory, and derived results on the topology of the moduli space of algebraic bundles over a complex algebraic curve. In this talk, I will discuss the Yang-Mills functional over a Klein surface (a 2-manifold equipped with a dianalytic structure) from the point of view of Morse theory, and derive results on the topology of the moduli space of real or quaternionic vector bundles over a real algebraic curve. This is based on joint work with Florent Schaffhauser.