Abstract: We review the proof of Narasimhan-Seshadri theorem on the correspondence between stable homomorphic vector bundles and irreducible unitary representations of Riemann surfaces as it was presented in the paper:

S.K. Donaldson, A new proof of a theorem of Narasimhan and Seshadri, J. Di fferential Geom. 18 (1983), 269-277.