This book, "Fundamentals of Semigroup Theory" by John M. Howie, provides a comprehensive introduction to the theory of semigroups. It is structured into eight chapters, each covering different aspects of semigroup theory. The first chapter introduces basic concepts, including monogenic semigroups, ordered sets, binary relations, congruences, free semigroups, and ideals. The second chapter discusses Green's equivalences and regular semigroups, focusing on the structure of D-classes and regular semigroups. The third chapter explores 0-simple semigroups, including the Rees theorem, completely simple semigroups, and congruences on these structures. The fourth chapter delves into completely regular semigroups, covering the Clifford decomposition, Clifford semigroups, bands, and free bands. The fifth chapter is dedicated to inverse semigroups, discussing natural order relations, congruences, Munn semigroups, and free inverse monoids. The sixth chapter covers other classes of regular semigroups, such as locally inverse, orthodox, and semibands. The seventh chapter focuses on free semigroups, including their properties and codes. The eighth chapter examines semigroup amalgams, including systems, free products, dominions, and the extension property. The book also includes exercises and notes at the end of each chapter, along with a list of references, symbols, and an index. The content is suitable for students and researchers in mathematics, particularly those interested in semigroup theory.This book, "Fundamentals of Semigroup Theory" by John M. Howie, provides a comprehensive introduction to the theory of semigroups. It is structured into eight chapters, each covering different aspects of semigroup theory. The first chapter introduces basic concepts, including monogenic semigroups, ordered sets, binary relations, congruences, free semigroups, and ideals. The second chapter discusses Green's equivalences and regular semigroups, focusing on the structure of D-classes and regular semigroups. The third chapter explores 0-simple semigroups, including the Rees theorem, completely simple semigroups, and congruences on these structures. The fourth chapter delves into completely regular semigroups, covering the Clifford decomposition, Clifford semigroups, bands, and free bands. The fifth chapter is dedicated to inverse semigroups, discussing natural order relations, congruences, Munn semigroups, and free inverse monoids. The sixth chapter covers other classes of regular semigroups, such as locally inverse, orthodox, and semibands. The seventh chapter focuses on free semigroups, including their properties and codes. The eighth chapter examines semigroup amalgams, including systems, free products, dominions, and the extension property. The book also includes exercises and notes at the end of each chapter, along with a list of references, symbols, and an index. The content is suitable for students and researchers in mathematics, particularly those interested in semigroup theory.