Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing a framework for saying when one thing is "less than" or "precedes" another.

An alphabetical list of many notions of order theory can be found in the order theory glossary. See also inequality, extreme value and mathematical optimization.


Distinguished elements of partial orders

Subsets of partial orders

Special types of partial orders


Completeness properties

Orders with further algebraic operations

Orders in algebra

Functions between partial orders

Completions and free constructions

Domain theory

Main article: Domain theory

Orders in mathematical logic

Orders in topology