Correlation in partially ordered sets

Correlation in partially ordered sets is a very active research area. The paper reviews basic results for correlation within ordered sets that focus on distributive lattices, systems of subsets ordered by proper inclusion, and the family of linear extensions of an arbitrary finite ordered set. Included are the Ahlswede-Daykin theorem, the FKG theorem, the nonstrict and strict xyz inequalities, and the universal correlation theorems of Winkler and Brightwell. The paper also mentions several corollaries and applications, and notes some open problems. Proofs of many of the theorems are included.