1. Invariants and moduli; 2. Rings and polynomials; 3. Algebraic varieties; 4. Algebraic groups and rings of invariants; 5. Construction of quotient spaces; 6. Global construction of quotient varieties; 7. Grassmannians and vector bundles; 8. Curves and their Jacobians; 9. Stable vector bundles on curves; 10. Moduli functors; 11. Intersection numbers and the Verlinde formula; 12. The numerical criterion and its applications.
This 2003 volume consists of the first two volumes of Mukai's series on moduli theory.
'The book contains a great amount of material, but it remains very readable. The author has obviously put a lot of effort into making even the complicated topics accessible.' G r Megyesi, UMIST