The Special Orthogonal Group, denoted as SO(n), is a mathematical group that consists of all n x n orthogonal matrices with a determinant of 1. These matrices represent rotations in n-dimensional space, preserving both distances and orientations. The group is important in various fields, including physics and computer graphics, where understanding rotations is essential. The elements of SO(n) can be thought of as transformations that rotate vectors without changing their length. For example, in SO(3), which deals with three-dimensional space, these transformations can describe the rotation of objects in 3D space, making it a fundamental concept in mechanics and robotics.