Linear Algebraic Monoids

Background.- Algebraic Monoids.- Regularity Conditions.- Classification of Reductive Monoids.- Universal Constructions.- Orbit Structure of Reductive Monoids.- The Analogue of the Bruhat Decomposition.- Representations and Blocks of Algebraic Monoids.- Monoids of Lie Type.- Cellular Decomposition of Algebraic Monoids.- Conjugacy Classes.- The Centralizer of a Semisimple Element.- Combinatorics Related to Algebraic Monoids.- Survey of Related Developments.