This is a self-contained exposition by way of one of many major specialists in lattice theory, George Grätzer, offering the key result of the final 70 years on congruence lattices of finite lattices, that includes the author's signature Proof-by-Picture method.

Key features:

* Insightful dialogue of strategies to build "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions

* comprises whole proofs, an in depth bibliography and index, and over a hundred and forty illustrations

* This new version contains new components on Planar Semimodular Lattices and The Order of precept Congruences, protecting the examine of the final 10 years

The publication is acceptable for a one-semester graduate path in lattice concept, and it's a functional reference for researchers learning lattices.

**Reviews of the 1st edition:**

"There exist loads of attention-grabbing ends up in this zone of lattice concept, and a few of them are awarded during this e-book. [This] monograph…is an excellent paintings in lattice conception, like every the contributions through this writer. … the best way this publication is written makes it tremendous attention-grabbing for the experts within the box but additionally for the scholars in lattice idea. furthermore, the writer offers a chain of significant other lectures which support the reader to procedure the Proof-by-Picture sections." **(Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica, Vol. LII (1), 2007)**

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"The ebook is self-contained, with many special proofs offered that may be step by step. [I]n addition to giving the complete formal information of the proofs, the writer chooses a by some means extra pedagogical approach that he calls Proof-by-Picture, someway with regards to the combinatorial (as against algebraic) nature of the various offered effects. i feel that this ebook is a much-needed software for any mathematician wishing a gradual creation to the sector of congruences representations of finite lattices, with emphasis at the extra 'geometric' aspects." —**Mathematical Reviews**