Ring theory is a branch of abstract algebra that studies algebraic structures known as rings. A ring consists of a set equipped with two operations: addition and multiplication. These operations must satisfy certain properties, such as associativity and distributivity, allowing for the exploration of various mathematical concepts. In ring theory, important types of rings include commutative rings, where multiplication is commutative, and rings with unity, which have a multiplicative identity. Ring theory has applications in various fields, including number theory, geometry, and cryptography, providing a framework for understanding mathematical relationships and structures.