Birkhoff G. Lattice Theory

3rd Ed. — NY.: American Mathematical Society, 1967. — 418 p. [1st Ed., 1940; 2nd (Revised) Ed., 1948], English. Interactive menu. (OCR-слой).Preface to the Third Edition.
The purpose of this edition is threefold: to make the deeper ideas of lattice theory accessible to mathematicians generally, to portray its structure, and to indicate some of its most interesting applications. As in previous editions, an attempt is made to include current developments, including various unpublished ideas of my own; however, unlike previous editions, this edition contains only a very incomplete bibliography.
I am summarizing elsewhere my ideas about the role played by lattice theory in mathematics generally. I shall therefore discuss below mainly its logical structure, which I have attempted to reflect in my table of contents.
The beauty of lattice theory derives in part from the extreme simplicity of its basic concepts: (partial) ordering, least upper and greatest lower bounds. In this respect, it closely resembles group theory. These ideas are developed in Chapters I-V below, where it is shown that their apparent simplicity conceals many subtle variations including for example, the properties of modularity, semimodularity, pseudo-complements and orthocomplements.Types of Lattices.
Postulates for Lattices.
Structure and Representation theory.
Geometric Lattices.
Complete Lattices.
Universal Algebra.
Applications to Algebra.
Transfinite Induction.
Applications to General Topology.
Metric and Topological Lattices.
Borel Algebras and von Neumann Lattices.
Applications to Logic and Probability.
Lattice-Ordered Group.
Lattice-Ordered Monoids.
Vector Lattices.
Positive Linear Operators.
Lattice-Ordered Rings.