本书是对平面代数曲线的一个非正式且通俗易懂的介绍，也是代数几何的一个自然切入点。这本书有一个统一的主题：给曲线足够的生存空间，美丽的定理就会随之而来。这本书通过具体的例子和图片介绍抽象的概念，为读者提供了对主题的坚实直觉，同时保持了阐述的简单易懂。它可以作为平面代数曲线本科课程的教材，也可以作为研究生代数几何的配套教材。数学背景有限的人可以阅读这本书。这是因为对于数学之外的人来说，对代数几何的入门需求越来越大，代数几何在从生物学到化学、机器人到密码学等领域发挥着越来越大的作用。

前辅文
1 A Gallery of Algebraic Curves
  1.1 Curves of Degree One and Two
  1.2 Curves of Degree Three and Higher
  1.3 Six Basic Cubics
  1.4 Some Curves in Polar Coordinates
  1.5 Parametric Curves
  1.6 The Resultant
  1.7 Back to an Example
  1.8 Lissajous Figures
  1.9 Morphing Between Curves
  1.10 Designer Curves
2 Points at Infinity
  2.1 Adjoining Points at Infinity
  2.2 Examples
  2.3 A Basic Picture
  2.4 Basic Definitions
  2.5 Further Examples
3 From Real to Complex
  3.1 Definitions
  3.2 The Idea of Multiplicity; Examples
  3.3 A Reality Check
  3.4 A Factorization Theorem for Polynomials in C[x,y]
  3.5 Local Parametrizations of a Plane Algebraic Curve
  3.6 Definition of Intersection Multiplicity for Two Branches
  3.7 An Example
  3.8 Multiplicity at an Intersection Point of Two Plane Algebraic Curves
  3.9 Intersection Multiplicity Without Parametrizations
  3.10 Bézout's theorem
  3.11 Bézout's theorem Generalizes the Fundamental Theorem of Algebra
  3.12 An Application of Bézout's theorem: Pascal's theorem
4 Topology of Algebraic Curves in P2(C)
  4.1 Introduction
  4.2 Connectedness
  4.3 Algebraic Curves are Connected
  4.4 Orientable Two-Manifolds
  4.5 Nonsingular Curves are Two-Manifolds
  4.6 Algebraic Curves are Orientable
  4.7 The Genus Formula
5 Singularities
  5.1 Introduction
  5.2 Definitions and Examples
  5.3 Singularities at Infinity
  5.4 Nonsingular Projective Curves
  5.5 Singularities and Polynomial Degree
  5.6 Singularities and Genus
  5.7 A More General Genus Formula
  5.8 Non-Ordinary Singularities
  5.9 Further Examples
  5.10 Singularities versus Doing Math on Curves
  5.11 The Function Field of an Irreducible Curve
  5.12 Birational Equivalence
  5.13 Examples of Birational Equivalence
  5.14 Space-Curve Models
  5.15 Resolving a Higher-Order Ordinary Singularity
  5.16 Examples of Resolving an Ordinary Singularity
  5.17 Resolving Several Ordinary Singularities
  5.18 Quadratic Transformations
6 The Big Three: C, K, S
  6.1 Function Fields
  6.2 Compact Riemann Surfaces
  6.3 Projective Plane Curves
  6.4 f, f2, f: Curves and Function Fields
  6.5 g1, g2, g: Compact Riemann Surfaces and Curves
  6.6 h1, h2, h: Function Fields and Compact Riemann Surfaces
  6.7 Genus
  6.8 Genus 0
  6.9 Genus One
  6.10 An Analogy
  6.11 Equipotentials and Streamlines
  6.12 Differentials Generate Vector Fields
  6.13 A Major Difference
  6.14 Divisors
  6.15 The Riemann-Roch theorem
Bibliography
Index
About the Author