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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. Stablle vector bundles on curves 10. Moduli functors 11. Intersection numbers and the Verlinde formula 12. The numerical criterion and its applications.