This is an entry-in-progress for a new topic entry on order theory.

1. index of inequalities
2. partial ordering, linear ordering, pre-ordering, well-ordering
3. semilattices
4. general lattice theory
   1. modular lattices
   2. complemented lattices
   3. distributive lattices
5. lattices with operators
6. Boolean algebras
7. ordered algebraic structures
8. applications to topology, analysis
9. applications to mathematical logic, algebraic logic
10. applications to computer science, formal concept analysis