Quaternions are a number system that extends complex numbers, consisting of one real part and three imaginary parts. They are 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 representing rotations in three-dimensional space. In computer graphics and robotics, quaternions help avoid problems like gimbal lock, which can occur with traditional rotation methods. They provide a more efficient way to interpolate rotations, making them valuable in applications such as animation and flight simulation.