Add to ORKGScience is the process of seeking unity in the diversity of natural phenomenon. The purpose of this paper is to demonstrate that group theory brings unity to the theory of elementary particles. The prime motivations are first, to find a quantitative representation of the Lorentz transformation, and second, to find a quantitative representation of angular momentum. Since both of these have continuous parameters, groups with continuous parameters, particularly Lie groups, are of interest. The first portion of the paper develops the definition of Lie groups and their associated Lie algebras. The prerequisite definitions of transformations, groups, group representations, and continuous groups are given. The second portion of the paper presents ...