Vertex operator algebras (VOAs) are mathematical structures that arise in the study of two-dimensional conformal field theory and string theory. They consist of a vector space equipped with a vertex operator, which encodes information about the symmetries and states of a physical system. VOAs allow for the algebraic manipulation of these operators, facilitating the analysis of various physical phenomena. These algebras are characterized by their vertex operators, which can be thought of as generating functions for the states of a quantum system. They also include a grading by energy levels and a notion of locality, meaning that operators can be combined in a way that respects the physical principles of causality. VOAs have connections to other areas of mathematics, such as representation theory and modular forms.