Group theory is the study of algebraic structures called groups. By employing the concepts of group theory, chemists can study the symmetry of molecules. The possible symmetry elements and their matrix representations will be examined. Every molecule has a set of symmetry elements that make up a group. The symmetry groups of molecules and the relationship between chemistry and math terminology will be explored. Group theory and the symmetry of molecules have many practical applications in chemistry, such as understanding vibrational spectroscopy and crystallography.