The Unitary Group is a mathematical concept in the field of group theory, which studies the algebraic structures known as groups. Specifically, the Unitary Group consists of all unitary matrices, which are square matrices that, when multiplied by their conjugate transpose, yield the identity matrix. This property makes unitary matrices important in various areas of mathematics and physics, particularly in quantum mechanics. Unitary Groups are denoted as U(n), where "n" represents the dimension of the matrices. They play a crucial role in preserving inner products, making them essential for transformations that maintain the geometric structure of vector spaces. Applications of Unitary Groups can be found in areas such as quantum computing and signal processing.