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This book now in its second revised and extended edition is a self-contained exposition of the theory of compact right semigroupsfor discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra, and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more.

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic.

Editorial Board

Lev Birbrair,...

Thisbook gives a coherent account of the theory of Banach spaces and Banachlattices, using the spaces C_0(K) of continuous functions on a locallycompact space K as the main example. It gives severalnew constructions, some involving Boolean rings, of this space as well as many results on theStonean space of Boolean rings.