This comprehensive, encyclopedic text in four parts aims to give the reader - from the graduate student to the researcher/practitioner - a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, thereby updating and modernizing the semigroup theory literature.

"This comprehensive, encyclopedic text in four parts aims to give the reader - from the graduate student to the researcher/practitioner - a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, thereby updating and modernizing the semigroup theory literature."

-Preface.- List of Tables.-List of Figures.-Introduction.-Part I. The q-operator and Pseudovarieties of Relational Morphisms.-1. Foundations for Finite Semigroup Theory.-2. The q-operator - 3.The Equational Theory -Part II. Complexity in Finite Semigroup Theory. -4. The Complexity of Finite Semigroups. -5. Two-Sided Complexity and the Complexity of Operators.-Part III. The Algebraic Lattice of Semigroup Pseudovarieties.-6. Algebraic Lattices, Continuous Lattices and Closure Operators.-7. The Abstract Spectral Theory of PV.-Part IV. Quantales, Indempotent Semirings, Matrix Algebras and the Triangular Product-8. Quantales.-9. The Triangular Product and Decomposition Results for Semirings.-A. The Green-Rees Local Structure Theory.-B. Tables on Preservation of Sups and Infs.- List of Problems.- References.- Table of Pseudovarieties.-Table of Operators and Products.-Index of Notation.-Author Index.-Index.