This first text on the subject provides a comprehensive introduction to the representation
theory of finite monoids. Carefully worked examples and exercises provide the bells and
whistles for graduate accessibility bringing a broad range of advanced readers to the
forefront of research in the area. Highlights of the text include applications to probability
theory symbolic dynamics and automata theory. Comfort with module theory a familiarity with
ordinary group representation theory and the basics of Wedderburn theory are prerequisites
for advanced graduate level study. Researchers in algebra algebraic combinatorics automata
theory and probability theory will find this text enriching with its thorough presentation of
applications of the theory to these fields. Prior knowledge of semigroup theory is not expected
for the diverse readership that may benefit from this exposition. The approach taken in this
book is highly module-theoretic and follows the modern flavor of the theory of finite
dimensional algebras. The content is divided into 7 parts. Part I consists of 3 preliminary
chapters with no prior knowledge beyond group theory assumed. Part II forms the core of the
material giving a modern module-theoretic treatment of the Clifford -Munn-Ponizovskii theory of
irreducible representations. Part III concerns character theory and the character table of a
monoid. Part IV is devoted to the representation theory of inverse monoids and categories and
Part V presents the theory of the Rhodes radical with applications to triangularizability. Part
VI features 3 chapters devoted to applications to diverse areas of mathematics and forms a high
point of the text. The last part Part VII is concerned with advanced topics. There are also 3
appendices reviewing finite dimensional algebras group representation theory and Möbius
inversion.
