1. Finite generation of invariants; 2. Poincare series; 3. Divisor classes, ramification and hyperplanes; 4. Homological properties of invariants; 5. Polynomial tensor exterior algebra; 6. Polynomial rings and regular local rings; 7. Groups generated by pseudoreflections; 8. Modular invariants; Appendices; Bibliography; Index.
This is the first book to deal with invariant theory and the representations of finite groups.
"...not only complete, it is written with a view to its being consulted on page 49 without having read up to page 48. It contains a wealth of material in updated form which should give a great impulse to further work, for example, an account of Dickson's work on invariants under the classical groups over finite fields." G.-C. Rota, Bulletin of Mathematics Books "...The exposition is uniformly excellent. It is also worth observing that many important ideas in modern commutative algebra were developed in connection with invariant theory and arise in the proofs cited...The author gives detailed, textbook-like explanations of all of these. As is customary for books published by Cambridge University Press in this series, the typography sets a standard of excellence and the price is remarkably low." Frank Grosshans, Mathematical Reviews