This book started with Lattice Theory, First Concepts, in 1971. Then
came General Lattice Theory, First Edition, in 1978, and the Second
Edition twenty years later. Since the publication of the first edition
in 1978, General Lattice Theory has become the authoritative
introduction to lattice theory for graduate students and the standard
reference for researchers. The First Edition set out to introduce and
survey lattice theory. Some 12,000 papers have been published in the
field since then; so Lattice Theory: Foundation focuses on introducing
the field, laying the foundation for special topics and applications.
Lattice Theory: Foundation, based on the previous three books, covers
the fundamental concepts and results. The main topics are
distributivity, congruences, constructions, modularity and
semimodularity, varieties, and free products. The chapter on
constructions is new, all the other chapters are revised and expanded
versions from the earlier volumes. Almost 40 "diamond sections'', many
written by leading specialists in these fields, provide a brief glimpse
into special topics beyond the basics. "Lattice theory has come a long
way... For those who appreciate lattice theory, or who are curious about
its techniques and intriguing internal problems, Professor Grätzer's
lucid new book provides a most valuable guide to many recent
developments. Even a cursory reading should provide those few who may
still believe that lattice theory is superficial or naive, with
convincing evidence of its technical depth and sophistication."
Bulletin of the American Mathematical Society "Grätzer's book General
Lattice Theory has become the lattice theorist's bible." Mathematical
Reviews
