Recently developed techniques in semigroup theory are introduced in a single self-contained volume. The trend is from the abstract to the combinatorial, with new probalistic and word-problem results of interest to students of computer science and algebra alike. The richness of the field is illustrated through 170 exercises.

Fundamentals; Free inverse semigroups and the theorems of McAlister; Biordered sets; Zigzags and their applications; Semigroup diagrams and word problems; Combinatorial aspects of transformation semigroups; References; Glossary of notation; Index.

'This book introduces recently developed ideas in semigroup theory and serves to provide a handy reference guide previously unavailable in a single volume.' L'Enseignement Mathématique, 1992 'fresh and well-written book ... Graphical and diagram arguments make proofs intuitive and elegant.' J. Henno, Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts 'Nearly two thirds of the content appear here for the first time in book-form, written in a fresh and stimulating style. New emphases and new connections in the presentation make this book a pleasure to read.' H. Mitsch, Monatshelfe für Mathematik, Vol. 116, No. 2, 1993 'Refreshingly lively and down-to-earth, with many new results (using semigroup diagrams to treat word problems) and new proofs, e.g., of Isbell's zigzag theorem, which is then applied to study amalgams.' Mathematika, 39 (1992) `The book is written with clarity, the proofs and arguments are usually presented in a brief and elegant way, and even familiar things are often viewed from a fresh perspective. Although the pace is fast, this enviably crisp and clear exposition is a pleasure to read. It will be very useful for semigroup theorists and graduate students as well as for specialists in other fields who may use it as a reference. Altogether, this is a most welcome addition to the available monographs on semigroups.' Boris M. Schein, Semigroup Forum Vol. 49 (1994)