Reflection groups and Coxeter groups / James E. Humphreys

This is a useful book. The style is informal and the arguments are clear. The publisher describes it as a "graduate textbook'' accessible to a reader with "a good knowledge of algebra'' which "attempts to be both an introduction to Bourbaki and an updating of the coverage''. This is fair billing. In its 200 pages it gives a readable introduction to Coxeter groups. It is the unique graduate level text on this subject and most of what it does is important for various aspects of Lie theory. The author keeps prerequisites to a minimum: the Euler characteristic of the Coxeter complex is computed without any topology and the section on invariants is written without any technicalities from commutative algebra or character theory. Occasional remarks hint at deeper connections with Lie theory. ... (MathSciNet)

Bibliogr. p. 185-202. Index