Gratzer G. The Congruences of a Finite Lattice.A Proof-by-Picture Appr. 3ed 2023

Textbook in PDF format

The congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems. Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years ! It features the author’s signature “Proof-by-Picture” method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner.
Key features include:
An insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions.
Complete proofs, an extensive bibliography and index, and over 180 illustrations.
Additional chapters covering new results of the last seven years, increasing the size of this edition to 430 pages, 360 statements, and 262 references.
This text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices