The Riemann-Roch theorem

In the mid- 19th century, B. Riemann introduced the notion of Riemann surface in his Ph.D thesis on complex analysis. Together with non-Euclidean geometry, the theory of Riemann surface is a germination of modern geometry in both algebraic and analytic sense. In this talk, I will give an introduction of the theory of Riemann surface centering around the Riemann-Roch theorem. It is an important prototype of the Atiyah-Singer index theorem, the starting point of my research field.