Riemann-roch Theorem And Its Application

The thesis started with a brief introduction to the terminologies involved with the RiemannRoch Theorem,including divisors,meromorphic functions,and meromorphic differentials.Then it was followed by the statement of the Riemann-Roch Theorem and its corollaries.After that we introduced the classic Riemann-Hurwitz Formula,and give a proof of it using the Riemann-Roch Theorem.In the last part of the thesis,we introduced an interesting question on Riemann surfaces,namely,the problem of Weierstrass gap numbers,and we used the Riemann-Roch Theorem to solve it.