What are resources on invariant theory? Basically I've run into a need to teach myself some of the basics of invariant theory and was looking for a good place to start. I'd prefer online / freeish resources if anyone knows of any that can be trusted - otherwise if someone can recommend a good introductory book on the subject that would be most appreciated.


(Currently considering getting or perhaps convincing my library to order for me P. Olivers Classical Invariant Theory - but I thought I'd ask around first).


As a second question - two in one if you will - and perhaps this will help to let you know how little I know about invariant theory - can anyone quickly summarize the difference between Classical and Geometric Invariant Theory? Presently I am thinking what I need is the classical kind - but again more information is always helpful.


P.S. Geometric invariant theory may not have been the best tag for this question, but apparently new users can't create new tags, so I picked the closest one - anyone that has the power to change the tag to something more appropriate please do so.



Resources on invariant theory
Usual invariant theory is dedicated to studying rings; a good example of a result from classical invariant theory is that the ring of invariant polynomials on any representation of a reductive group is finitely generated.


Geometric invariant theory is about constructing and studying the properties of certain kinds of quotients; a good example would be the moduli space of semi-stable vector bundles on an algebraic variety.


In my mind, the difference is this: Classical invariant theory is a collection of results about the interaction between group actions and commutative algebra. Geometric invariant theory is a technique for constructing interesting spaces.


