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 Graetzer'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 "Graetzer's book General Lattice Theory has become the lattice theorist's bible." Mathematical Reviews
Industry Reviews
From the reviews:"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 Gratzer'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." Garrett Birkhoff (Bulletin of the American Mathematical Society "Gratzer's book General Lattice Theory has become the lattice theorist's bible." (Mathematical Reviews) "This book has a long history maturing in contents and details over a period of more than 40 years. ... For many years to come it will be the standard textbook and main reference for everybody interested in Lattice Theory. ... It contains more than 1,000 exercises, a bibliography of 742 items, and a useful glossary of notation. All this, together with the very clear style of presentation, makes the book an extremely valuable contribution to the theory of lattices." (M. Mitsch, Monatshefte fur Mathematik, Vol. 164 (4), 2011)
