第一部分讲积分的周期和Hodge结构，由两位作者撰写，可能仅用解析的观点；第二部分讲曲线及其雅可比簇，这方面的书原已有多本(如Mumford的书),而在本书中接近用解析的观点，由一位作者撰写。本书适合复代数几何、复几何方面的研究生和专业研究人员作为参考书。

Introduction
Chapter 1.Classical Hodge Theory
1.Algebraic Varieties
2.Complex Manifolds
3.A Comparison Between Algebraic Varieties and Analytic Spaces
4.Complex Manifolds as C Manifolds
5.Connections on Holomorphic Vector Bundles
6.Hermitian Manifolds
7.Kahler Manifolds
8.Line Bundles and Divisors
9.The Kodaira Vanishing Theorem
10.Monodromy
Chapter 2.Periods of Integrals on Algebraic Varieties
1.Classifying Space
2.Complex Tori
3.The Period Mapping
4.Variation of Hodge Structures
5.Torelli Theorems
6.Infinitesimal Variation of Hodge Structures
Chapter 3.Torelli Theorems
1.Algebraic Curves
2.The Cubic Threefold
3.K3 Surfaces and Elliptic Pencils
4.Hypersurfaces
5.Counterexamples to Torelli Theorems
Chapter 4.Mixed Hodge Structures
1.Definition of mixed Hodge structures
2.Mixed Hodge structure on the Cohomology of a Complete Variety with Normal Crossings
3.Cohomology of Smooth Varieties
4.The Invariant Subspace Theorem
5.Hodge Structure on the Cohomology of Smooth Hypersurfaces
6.Further Development of the Theory of Mixed Hodge Structures
Chapter 5.Degenerations of Algebraic Varieties
1.Degenerations of Manifolds
2.The Limit Hodge Structure
3.The Clemens—Schmid Exact Sequence
4.An Application of the Clemens—Schmid Exact Sequence to the Degeneration of Curves
5.An Application of the Clemens—Schmid Exact Sequence to
Surface Degenerations.The Relationship Between the Numerical
Invariants of the Fibers Xt and XO
6.The Epimorphicity of the Period Mapping for K3 Surfaces
Comments on the bibliography
References
Index