Module Theory is a branch of mathematics that studies modules, which are generalizations of vector spaces. In this context, a module is a mathematical structure consisting of a set equipped with an operation that combines elements of the set with elements from a ring, similar to how vector spaces combine elements with scalars from a field. This theory helps in understanding algebraic structures and their relationships. One of the key concepts in Module Theory is the idea of submodules, which are subsets of modules that themselves form modules under the same operations. This concept is analogous to subspaces in vector spaces. Module Theory has applications in various areas of mathematics, including algebra, geometry, and number theory.