George Gratzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Gratzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished...

George Gratzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998).

This three-volume-set comprises the complete lattice theory project.

Volume 1 of the set, Lattice Theory: Foundation, is the revised and enlarged third edition of General Lattice Theory. It focuses on introducing the field and covers the fundamental concepts and results.

The two Special Topics and Applications volumes (volumes 2 and 3 of the set), jointly edited by George Gratzer and Friedrich Wehrung, update the reader on some of the vast areas not in Foundation.

Volume 1 is divided into three parts. Part I. Topology and Lattices includes...

Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings.