This is a self-contained exposition by one of the leading experts in
lattice theory, George Grätzer, presenting the major results of the last
70 years on congruence lattices of finite lattices, featuring the
author's signature Proof-by-Picture method.
Key features:
* Insightful discussion of techniques to construct "nice" finite
lattices with given congruence lattices and "nice" congruence-preserving
extensions
* Contains complete proofs, an extensive bibliography and index, and
over 140 illustrations
* This new edition includes two new parts on Planar Semimodular
Lattices and The Order of Principle Congruences, covering the research
of the last 10 years
The book is appropriate for a one-semester graduate course in lattice
theory, and it is a practical reference for researchers studying
lattices.
Reviews of the first edition:
"There exist a lot of interesting results in this area of lattice
theory, and some of them are presented in this book. [This]
monograph...is an exceptional work in lattice theory, like all the
contributions by this author. ... The way this book is written makes it
extremely interesting for the specialists in the field but also for the
students in lattice theory. Moreover, the author provides a series of
companion lectures which help the reader to approach the
Proof-by-Picture sections." (Cosmin Pelea, Studia Universitatis
Babes-Bolyai Mathematica, Vol. LII (1), 2007)
"The book is self-contained, with many detailed proofs presented that
can be followed step-by-step. [I]n addition to giving the full formal
details of the proofs, the author chooses a somehow more pedagogical way
that he calls Proof-by-Picture, somehow related to the combinatorial (as
opposed to algebraic) nature of many of the presented results. I believe
that this book is a much-needed tool for any mathematician wishing a
gentle introduction to the field of congruences representations of
finite lattices, with emphasis on the more 'geometric' aspects."
--Mathematical Reviews
