Algebraic Monoids Group Embeddings and Algebraic Combinatorics On Algebraic Semi groups and Monoids (M. Brion) Algebraic Semi groups are Strongly π regular (M. Brion L. E. Renner) Rees Theorem and Quotients in Linear Algebraic Semi groups (M. S. Putcha) Representations of Reductive Normal Algebraic Monoids (S. Doty) On Linear Hodge Newton Decomposition for Reductive Monoids (S. Varma) The Structure of Affine Algebraic Monoids in Terms of Kernel Data (W. Huang) Algebraic Monoids and Renner Monoids (Z. Li Z. Li Y. Cao) Conjugacy Decomposition of Canonical and Dual Canonical Monoids (R. K. Therkelsen) The Endomorphisms Monoid of a Homogeneous Vector Bundle (L. Brambila Paz and A. Rittatore) On Certain Semi groups Derived from Associative Algebras (J. Okniński) The Betti Numbers of Simple Embeddings (L. E. Renner) SL(2) regular Subvarieties of Complete Quadratics (M. B. Can M. Joyce) Markov Chains for Promotion Operators (A. Ayyer S. Klee A. Schilling) Fomin Greene Monoids and Pieri Operations (C. Benedetti N. Bergeron) Affine Permutations and an Affine Catalan Monoid (T. Denton) 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: v structure and representation theory of reductive algebraic monoids v monoid schemes and applications of monoids v monoids related to Lie theory v equivariant embeddings of algebraic groups v constructions and properties of monoids from algebraic combinatorics v endomorphism monoids induced from vector bundles v 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contained introduction to these topics while the remaining contributions are research articles containing previously unpublished results which are sure to become very influential for future work.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 semigroups are strongly π 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