Representation theory, the mathematical study of symmetry and its manifestations in various systems, has its roots in two key developments: the late nineteenth-century examination of groups of linear transformations and the early twentieth-century advent of quantum mechanics. Its influence has become an essential tool in mathematics, physics, and chemistry. Furthermore, representation theory has been enriched by concepts from theoretical physics, culminating in a comprehensive synthesis of diverse mathematical fields by the end of the 20th century. This includes Lie algebras and quantum groups, automorphic forms, finite groups, and the topology of knots and 3-varieties. A key component of this synthesis is a category of algebraic structures known as vertex algebras. The project seeks to further the understanding of vertex algebras and elucidate the connections between the aforementioned areas.