0. Preliminaries.- 1. Definitions.- 2. First properties.- 3. Good and bad actions.

- 4. Further properties.- 5. Resumé of some results of Grothendieck.- 1. Fundamental theorems for the actions of reductive groups.- 1. Definitions.

- 2. The affine case.- 3. Linearization of an invertible sheaf.- 4. The general case.- 5. Functional properties.

- 2. Analysis of stability.- 1. A numeral criterion.- 2. The flag complex.- 3. Applications.

- 3. An elementary example.- 1. Pre-stability.- 2. Stability.- 4. Further examples.

- 1. Binary quantics.- 2. Hypersurfaces.- 3. Counter-examples.- 4. Sequences of linear subspaces.

- 5. The projective adjoint action.- 6. Space curves.- 5. The problem of moduli -- 1st construction.- 1. General discussion.

- 2. Moduli as an orbit space.- 3. First chern classes.- 4. Utilization of 4.6.- 6.

Abelian schemes.- 1. Duals.- 2. Polarizations.- 3. Deformations.- 7.

The method of covariants -- 2nd construction.- 1. The technique.- 2. Moduli as an orbit space.- 3. The covariant.- 4.

Application to curves.- 8. The moment map.- 1. Symplectic geometry.- 2. Symplectic quotients and geometric invariant theory.- 3.

Kähler and hyperkähler quotients.- 4. Singular quotients.- 5. Geometry of the moment map.- 6. The cohomology of quotients: the symplectic case.- 7.

The cohomology of quotients: the algebraic case.- 8. Vector bundles and the Yang-Mills functional.- 9. Yang-Mills theory over Riemann surfaces.- Appendix to Chapter 1.- Appendix to Chapter 2.- Appendix to Chapter 3.

- Appendix to Chapter 4.- Appendix to Chapter 5.- Appendix to Chapter 7.- References.- Index of definitions and notations.