《代数几何（英文版）》提供了一个抽象代数几何的介绍使用的方法的方案和上同调主要研究对象是代数闭域上仿射空间或射影空间中的代数簇，这些在第一章中介绍，建立一些基本概念和例子。那么方案和上同调的方法在第二章和第三章中发展，重点是应用而不是过度概括性。概括性书的最后两章（第四章和第五章）用这些方法来研究经典代数曲线曲面理论中的课题。

Introduction
CHAPTER Ⅰ Varieties
1 Affine Varieties
2 Projective Varieties
3 Morphisms
4 Rational Maps
5 Nonsingular Varieties
6 Nonsingular Curves
7 Intersections in Projective Space
8 What Is Algebraic Geometry?

CHAPTER Ⅱ Schemes
1 Sheaves
2 Schemes
3 First Properties of Schemes
4 Separated and Proper Morphisms
5 Sheaves of Modules
6 Divisors
7 Projective Morphisms
8 Differentials
9 Formal Schemes

CHAPTER Ⅲ Cohomology
1 Derived Functors
2 Cohomology of Sheaves
3 Cohomology of a Noetherian Afine Scheme
4 Cech Cohomology
5 The Cohomology of Projective Space
6 Ext Groups and Sheaves
7 The Serre Duality Theorem
8 Higher Direct Images of Sheaves
9 Flat Morphisms
10 Smooth Morphisms
11 The Theorem on Formal Functions
12 The Semicontinuity Theorem

CHAPTER Ⅳ Curves
1 Riemann-Roch Theorem
2 Hurwitz's Theorem
3 Embeddings in Projective Space
4 Elliptic Curves
5 The Canonical Embedding
6 Classification of Curves in P3

CHAPTER Ⅴ Surfaces
1 Geometry on a Surface
2 Ruled Surfaces
3 Monoidal Transformations
4 The Cubic Surface in P3
5 Birational Transformations
6 Classification of Surfaces

APPENDIX A Intersection Theory
1 Intersection Theory
2 Properties of the Chow Ring