Table of Contents

1. The symbolic method; 2. The first fundamental theorem; 3. Reductive algebraic groups; 4. Hilbert's fourteenth problem; 5. Algebra of covariants; 6. Quotients; 7. Linearization of actions; 8. Stability; 9. Numerical criterion of stability; 10. Projective hypersurfaces; 11. Configurations of linear subspaces; 12. Toric varieties.

Promotional Information

This 2003 book is a brief introduction to algebraic and geometric invariant theory with numerous examples and exercises.

Reviews

'The exposition is very systematic, lucid and sufficiently detailed. it certainly [reflects] the author's passion, versatility, all-round knowledge in mathematics, and mastery as both an active researcher and devoted teacher. It is very gratifying to see this beautiful, modern and still down-to-earth introduction to classical and contemporary invariant theory at the public's disposal ...' Zentralblatt fur Mathematik 'Besides interested graduate students and experts, I recommend the book also to mathematicians and theoretical physicists whose research may require invariant theory, representation theory or algebraic geometry.' Acta Scientiarum Mathematicarum