We accredit discovery of quaternions to the Irish mathematician and physicist William Rowan Hamilton who, motivated by the role of the set of complex numbers in plane geometry, sought to obtain an algebraic structure that would have a similar role in space geometry. In his honor, the set of quaternions is denoted by \(\mathbb{H}\). Besides that set of quaternions forms a real vector space, it also forms a noncommutative unital ring, as quaternion multiplication is not commutative. The set of quaternions forms a specific algebraic structure called a division algebra. Quaternion division algebra is 4-dimensional real algebra and according to Frobenius’ theorem there are exactly three real division algebras:\(\mathbb{R}\), \(\mathbb{C}\) and \(\mathbb{H}\) . In addition, all division algebras have dimensions 1, 2, 4 or 8, but the only normed division algebras are \(\mathbb{R}\), \(\mathbb{C}\), \(\mathbb{H}\) and \(\mathbb{O}\), where \(\mathbb{O}\) denotes set of octonions - an 8-dimensional normed division algebra with nonassociative multiplication. Quaternions are associated with 3D rotations, which are usually implemented by the action of 3×3 orthogonal matrices with determinant 1. Elementary rotation matrices about fixed axes of the coordinate system are sufficient to bring an object to desired position in space, but a series of these rotations can lead to serious problem called gimbal lock. It follows from Euler’s theorem that every 3D rotation matrix (and products of these) can be written in terms of a rotation matrix \(R_{3}(\Theta,\tilde{n})\) which leaves the vector \(\tilde{n}\) fixed. It has a connection with the unit quaternion \(q(\Theta,\tilde{n}))=(cos\frac{\Theta}{2},\tilde{n}sin\frac{\Theta}{2})\). This form does not lead to gimbal lock anomalies.