Partition Theory is a branch of number theory that studies the ways in which a positive integer can be expressed as the sum of positive integers, disregarding the order of the addends. For example, the number 4 can be partitioned into 4, 3+1, 2+2, and 2+1+1, resulting in five distinct partitions. The theory was significantly developed by mathematicians like Srinivasa Ramanujan and G. H. Hardy. It has applications in various fields, including combinatorics and statistical mechanics, and is closely related to generating functions, which are used to encode partition information mathematically.