*Abstract: Riemann's mapping theorem was first announced with (sketch of) proof in his 1851 lecture in Gottingen. But that proof was not readily accepted by other mathematicians and was subsumed by the proof based upon the normal family method. This proof, now understood as the standard one, is not Riemann's but of Carathodory (Math. Ann. 1912) [later partly improved further by Fejer and Riesz]. In this lecture, I would like to present the precise version of Riemann's proof by Robert E. Greene and myself. Our proof stays at a level that does not exceed that of the beginning graduate student. Along the way, I would like also to discuss bits of history and remarks. [cf. R. E. Greene and K.-T. Kim, The Riemann mapping theorem from Riemann's viewpoint, Complex Analysis and its Synergies, 3:1 (2017) (Open access).]*

*Host: Steven Krantz*