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這一篇論文主要是介紹Riemann-Roch定理在緊黎曼面上的一些應用。特別地，我們證明每個緊黎曼都是代數簇。

This is an exposition of the Riemann-Roch theorem and its application to the study of compact Riemann surfaces.In particular, we show that all compact Riemann surfaces are algebraic.

1　Basic Definitions------------1
2　Riemann-Roch Theorem--------10
3　Applications----------------16

[1]伍鴻熙, 緊黎曼曲面引論
[2]George Springer, Introduction to Riemann Surfaces
[3]Otto Forster, Lectures on Riemann Sufaces
[4]Farkas Kra, Riemann Surfaces
[5]Philip A. Griffiths, Introduction to Algebraic Curves
[6]Rick Miranda, Algebraic Curves and Riemann Surfaces
[7]Kenji Ueno, An Introduction to Algebraic Geometry
[8]Claude Chevaley, Introduction to the Theory of Algebraic Functions of One
Variable
[9]Kenkichi Iwasawa, Algebraic Functions
[10]Henning Stichtenoth, Algebraic Function Fields and Codes
[11]Klaus Fritzsche and Hans Grauert, From Holomorphic Functions to Complex
Manifolds