ABSTRACT
Partially ordered sets play important roles in a wide variety of applications, including the design of sorting and searching methods, the scheduling of tasks, the study of social choice, and the study of lattices. This chapter covers the basic concepts involving partially ordered sets, the various types of partially ordered sets, the fundamental properties of these sets, and their important applications. Lattices are posets with additional properties that capture some aspects of the intersection and the union of sets and of the greatest common divisor and least common multiple of positive integers. A chain is a subset of mutually comparable elements of a poset, or sometimes the subposet of poset formed by such a subset.
