The Congruences of a Finite Lattice

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This self-contained exposition by George Grätzer, a leading expert in lattice theory, presents significant results from the past 70 years on congruence lattices of finite lattices, utilizing the author's unique Proof-by-Picture method. Key features include insightful discussions on constructing "nice" finite lattices with specified congruence lattices and congruence-preserving extensions. The text contains complete proofs, an extensive bibliography, an index, and over 140 illustrations. This new edition adds two parts on Planar Semimodular Lattices and The Order of Principle Congruences, reflecting research from the last decade. Suitable for a one-semester graduate course in lattice theory, it also serves as a practical reference for researchers. Reviews of the first edition highlight the book's engaging presentation of interesting results in lattice theory, making it appealing to both specialists and students. The author offers companion lectures to facilitate understanding of the Proof-by-Picture sections. The book is described as self-contained, with detailed, step-by-step proofs that blend formal details with a pedagogical approach, emphasizing the geometric aspects of congruence representations of finite lattices, making it an essential resource for mathematicians.