Quaternions Algebra, Their applications in Rotations and Beyond Quaternions

Abstract: The theory of quaternions was discovered in the middle of nineteenth century and they were commonly used to represent rotations.This thesis is written to review the basic properties of quaternions algebra and their applications in representing rotation of a body in 3-dimensional Euclidean space. Also, last sections in this thesis explore why the use of quaternions are more advantages than Euler angle sequences and can quaternions themselves be further generalized to another number systems?