本書由世界圖書出版公司出版，主要內容包括：An Introduction to Elliptic Surfaces、Singular fibers、Singulex fibers of elliptic fibrations、lnvariants and the canonical bundle formula、Elliptic surfaces with a section and Weierstrass models、More general elliptic surfaces、The fundamental group等。

Preface
Introduction
1 Curves on a Surface
Introduction
Invariants of a surface
Divisors on a surface
Adjunetion and arithmetic genus
The Riemann-Roch formula
Algebraic proof of the Hodge index theorem
Ample and nef divisors
Exercises
2 Coherent Sheaves
What is a coherent sheaf?
A rapid review of Chern classes for projective varieties
Rank 2 bundles and sub-line bundles
Elementary modifications
Singularities of coherent sheaves
Torsion free and reflexive sheaves
Double covers
Appendix: some commutative algebra
Exercises
3 B|ratlonal Geometry
Blowing up
The Castelnuovo criterion and factorization of birational morphisms
Minimal models
More general contractions
Exercises
4 Stability
Definition of Mumford-Takemoto stability
Examples for curves
Some examples of stable bundles on p2
Gieseker stability
Unstable and semlstable sheaves
Change of polarization
The differential geometry of stable vector bundles
Exercises
5 Some Examples of Surfaces
Rational ruled surfaces
General ruled surfaces
Linear systems of cubics
An introduction to K3 surfaces
Exercises
6 Vector Bundles over Ruled Surfaces
Suitable ample divisors
Ruled sur faces
A brief introduction to local and global moduli
A Zariski open subeet of the moduli space
Exercises
7 An Introduction to Elliptic Surfaces
Singular fibers
Singulex fibers of elliptic fibrations
lnvariants and the canonical bundle formula
Elliptic surfaces with a section and Weierstrass models
More general elliptic surfaces
The fundamental group
Exercises
8 Vector Bundles over Elliptic Surfaces
Stable bundles on singular curves
Stable bundles of odd fiber degree over elliptie surface
A Zariski open subset of the modnii space
An overview of Donaldson invariants
The 2-dimensional invariant
Moduli spaces via extensions
Vector bundleswi thtrivial determinant
Even fiber degree and multiple fibers
Exercises
9 Bogomolov's Inequality and Applications
Statementofththeorem
The theorems of Bombieri and Reider
Theproof of Bogomolov's theorem
Symmetric powers of vector bundles on curves
Restriction the orems
Appendix:Galoisdes centtheory
Exercises
10 Classification of Algebraic Surfacesand of Stable Bundles
Outline of the classificationofs urfaces
Proof of Castelnuovo's theorem
The Albanese map
Proofs of the classification the oremsf or surfaces
The Castelnuovo-deFranchis theorem
Classification of threefolds
Classification of vector bundles
Exercises
References
Index