Lattice theory is a branch of mathematics that studies the structure of lattices, which are abstract algebraic systems. A lattice consists of a set of elements with a partial order, meaning that not all elements need to be comparable. In a lattice, any two elements have a unique least upper bound (called the join) and a greatest lower bound (called the meet). Lattices are used in various fields, including computer science, logic, and order theory. They help in understanding relationships between different elements and can model hierarchical structures, such as set theory and Boolean algebra.