The purpose of the third 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.

The 1996 reprint includes expanded and updated Additional References.

Table of Contents

• 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 groups
• Lattice-ordered monoids
• Vector lattices
• Positive linear operators
• Lattice-ordered rings
• Bibliography
• Index