本书是一部全面介绍代数曲线、代数流形的教程（全英文版）。主体内容有两部分组成：一部分以V.V.Shokurov所写的学术著作为蓝本，主要讲述黎曼面和代数曲面理论，深刻地揭示了黎曼面和其模型——复射影面中的复代数曲面的相互关系；另外一部分以V.I.Danilov的学术论文为蓝本主要讨论了代数变量及其概型。本书结构框架清晰，叙述简明扼要，可以帮助读者在很短的时间内了解并掌握代数几何的精华。

This book consists of two parts. The first is devoted to the theory of curves, which are treated from both the analytic and algebraic points of view. Starting with the basic notions of the theory of Riemann surfaces the reader is lead into an exposition covering the Riemann-Roch theorem, Riemann's fundamental existence theorem.uniformization and automorphic functions. The algebraic material also treats algebraic curves over an arbitrary field and the connection between algebraic curves and Abelian varieties. The second part is an introduction to higher- dimensional algebraic geometry. The author deals with algebraic varieties, the corresponding morphisms,the theory of coherent sheaves and, finally, The theory of schemes.This book is a very readable introduction to algebraic geometry and will be immensely useful to mathematicians working in algebraic geometry and complex analysis and especially to graduate students in these fields.

Ⅰ.Riemann Surfaces and Algebraic Curves

V.V.Shokurov

Ⅱ.Algebraic Varieties and Schemes

V.I.Danilov

Author Index

Subject Index