Beginning from a discussion of the known most fundamental dynamical structures of the Standard Model of physics, extended into the realms of mathematics and theory by the concept of "supersymmetry" or "SUSY," an introduction to efforts to develop a complete representation theory is given. Techniques drawing from graph theory, coding theory, Coxeter Groups, Riemann surfaces, and computational approaches to the study of algebraic varieties are briefly highlighted as pathways for future exploration and progress.