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The congruences of a lattice form the congruence lattice. In the past half-century, the study of congruence lattices has become a large and important field with a great number of interesting and deep results and many open problems. This self-contained exposition by one of the leading experts in lattice theory.Includes the latest findings from a pioneering researcher in the field. 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 nearly 80 open problems