Fano簇是代数几何中的一类重要研究对象，这方面的研究相当深入，有丰富的结果和技术性很强的工具。这一课题与数学物理有重要的联系。本书适合代数几何，特别是复代数几何方面的研究生和专业研究人员作为参考书，也可供物理等方面的专业人员参阅。

Introduction

Chapter 1. Preliminaries
1.1. Singularities
1.2. On Numerical Geometry of Cycles
1.3. On the Mori Minimal Model Program
1.4. Results on Minimal Models in Dimension Three

Chapter 2. Basic Properties of Fano Varieties
2.1. Definitions， Examples and the Simplest Properties
2.2. Some General Results
2.3. Existence of Good Divisors in the Fundamental Linear System
2.4. Base Points in the Fundamental Linear System

Chapter 3. Del Pezzo Varieties and Fano Varieties of Large Index
3.1. On Some Preliminary Results of Fujita
3.2. Del Pezzo Varieties. Definition and Preliminary Results
3.3. Nonsingular del Pezzo Varieties. Statement of the Main Theorem and Beginning of the Proof
3.4. Del Pezzo Varieties with Picard Number p=1 Continuation of the Proof of the Main Theorem
3.5. Del Pezzo Varieties with Picard Number p≥2 Conclusion of the Proof of the Main Theorem

Chapter 4. Fano Threefolds with p= 1
4.1. Elementary Rational Maps： Preliminary Results
4.2. Families of Lines and Conics on Fano Threefolds
4.3. Elementary Rational Maps with Center along a Line
4.4. Elementary Rational Maps with Center along a Conic
4.5. Elementary Rational Maps with Center at a Point
4.6. Some Other Rational Maps

Chapter 5. Fano Varieties of Coindex 3 with p= 1:The Vector Bundle Method
5.1. Fano Threefolds of Genus 6 and 8：Gushel's Approach
5.2. A Review of Mukai's Results on the Classification of Fano Manifolds of Coindex 3

Chapter 6. Boundedness and Rational Connectedness of Fano Varieties
6.1. Uniruledness
6.2. Rational Connectedness of Fano Varieties

Chapter 7. Fano Varieties with p≥ 2
7.1. Fano Threefolds with Picard Number p≥ 2 （Survey of Results of Mori and Mukai）
7.2. A Survey of Results about Higher-dimensional Fano Varieties with Picard Number p≥ 2

Chapter 8. Rationality Questions for Fano Varieties I
8.1. Intermediate Jacobian and Prym Varieties
8.2. Intermediate Jacobian： the Abel-Jacobi Map
8.3. The Brauer Groupas a Birational Invariant

Chapter 9. Rationality Questions for Fano Varieties II
9.1. Birational Automorphisms of Fano Varieties
9.2. Decomposition of Birational Maps in the Context of Mori Theory

Chapter 10. Some General Constructions of Rationality and Unirationality
10.1. Some Constructions of Unirationality
10.2. Unirationality of Complete Intersections
10.3. Some General Constructions of Rationality

Chapter 11. Some Particular Results and Open Problems
11.1. On the Classification of Three-dimensional -Fano Varieties
11.2. Generalizations
11.3. Some Particular Results
11.4. Some Open Problems

Chapter 12. Appendix： Tables
12.1. Del Pezzo Manifolds
12.2. Fano Threefolds with p= 1
12.3. Fano Threefolds with p= 2
12.4. Fano Threefolds with p= 3
12.5. Fano Threefolds with p= 4
12.6. Fano Threefolds with p≥ 5
12.7. Fano Fourfolds of Index 2 with p≥ 2
12.8. Toric Fano Threefolds

References
Index