An algebra 〈L;⋀, ⋁〉 is called a lattice if L is a nonempty set, ⋀ and ⋁ are binary operations on L, both ⋀ and ⋁ are idempotent, commutative, and associative, and they satisfy the absorption law. The study of lattices is called lattice theory. Note that this type of lattice is distinct from the regular array of points known as a point lattice (or informally as a mesh or grid). While every point lattice is a lattice under the ordering inherited from the plane, many lattices are not point lattices. Lattices offer a natural way to formalize and study the ordering of objects using a general concept known as the partially ordered set.

cubic lattice | distributive lattice | integration lattice | laminated lattice | lattice-ordered set | lattice theory | modular lattice | point lattice | toric variety