This extensively revised second edition of Inverse Semigroups offers a comprehensive and accessible introduction to the subject, aimed at graduate students and researchers across mathematics. First published in 1998 and still widely read, this seminal text has now been reorganized, updated, and expanded to reflect the many advances in the field over the past two decades. Inverse semigroup theory continues to play a central role in modern mathematics, with growing significance in operator algebras - particularly C*-algebras - as well as in group theory, topos theory, and the study of partial symmetries. This edition incorporates substantial new material, culminating in two brand new chapters, which brings the theory fully up to date. Topics include: Pseudogroups.; Self-similar actions.; Advances in non-commutative Stone duality.; Emerging links with C*-algebras and group theory.; Partial group actions.; Insights into the historical development of the theory.; With no other contemporary text focused solely on inverse semigroups and their broadening web of applications, this volume is an essential resource for both newcomers and seasoned researchers alike.