This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.

Topics presented include:

structure and representation theory of reductive algebraic monoids

monoid schemes and applications of monoids

monoids related to Lie theory

equivariant embeddings of algebraic groups

constructions and properties of monoids from algebraic combinatorics

endomorphism monoids induced from vector bundles

Hodge-Newton decompositions of reductive monoids

A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semi groups are strongly -regular.

Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics and the theory of algebraic group embeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings and algebraic combinatorics merged under the umbrella of algebraic monoids.