Quaternions are a mathematical system that extends complex numbers. They consist of one real part and three imaginary parts, typically represented as q = a + bi + cj + dk , where a, b, c, and d are real numbers, and i, j, k are the fundamental quaternion units. Quaternions are particularly useful in three-dimensional space for representing rotations. In computer graphics and robotics, quaternions help avoid problems like gimbal lock, which can occur with traditional rotation methods. They provide a smooth and efficient way to interpolate between orientations, making them essential in applications involving 3D modeling, animation, and aerospace engineering.