Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action

"This volume of the Encyclopaedia of Mathematical Sciences contains three contributions on actions of algebraic groups. The first one, by A. Bialynicki-Birula, is concerned with the general concept of a quotient, while the other two, by J.B.Carrell and W.M. McGovern, are on more specific topics. [...]

These three articles are all of value, but have somewhat different nature. Bialynicki-Birula's is a survey of a very wide area of research and requires much prior knowledge on the part of the reader. It is certainly not some something one could suggest as reading for a starting graduate student, but it is a useful reference for those who already have some knowledge and want to know about some aspect of the theory of quotients. The other two articles are much more accessible, especially that of McGovern, but could also be used as a source of general reference in the (more limited) areas they study."

P.Newstead, Liverpool, Jahresberichte der DMV, Vol. 107, Issue 4 (2005)