The Orthogonal Group is a mathematical concept that consists of all square matrices that preserve the length of vectors when transformed. Specifically, these matrices are orthogonal, meaning their rows and columns are orthonormal vectors. The group is denoted as O(n), where n represents the dimension of the space. Orthogonal transformations include rotations and reflections, which are essential in various fields such as physics, computer graphics, and robotics. The properties of the orthogonal group ensure that the inner product of vectors remains unchanged, making it crucial for maintaining geometric relationships in multidimensional spaces.