Group Theory is a branch of mathematics that studies the algebraic structures known as groups. A group is a set equipped with an operation that combines any two elements to form a third element, satisfying four fundamental properties: closure, associativity, identity, and invertibility. This framework allows mathematicians to analyze symmetry and structure in various mathematical contexts. One of the key applications of Group Theory is in understanding the symmetries of geometric objects. For instance, the dihedral group describes the symmetries of regular polygons, while Lie groups are used in physics to describe continuous symmetries. Group Theory has profound implications in many areas, including physics, chemistry, and cryptography.