This project examines the properties of the quaternions modulo n, written as H<sub>n</sub> which is defined as the set {a+bi+cj+dk | a,b,c,d∈Z<sub>n</sub> and i<sup>2</sup>=j<sup>2</sup>=k<sup>2</sup>=ijk=-1}. Particularly, this set forms a ring. Most of the project is devoted to classifying the groups of units for various n. First, a number of properties of units are proved for the quaternions and then some examples done in detail for small n. The order of the group of units is then proved for any n. Then, for the smaller n’s, the unit groups are classified. Other ring theoretic properties are also briefly examined.
