Linear Algebraic Monoids (Encyclopaedia of Mathematical Sciences)

This solid volume discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. Open problems are discussed as they arise and many useful exercises are included.

From the reviews:

"This account of algebraic monoids ... starts by recalling the basics of algebraic geometry, algebraic groups and semigroups ... . The main question, how a monoid is composed of units and idempotents, is discussed at length ... . A most useful account, giving current developments of the subject." (Mathematika, Vol. 52, 2005)