This advanced text introduces the foundations, interpretations, and data-analytic applications of symmetry studies in optical sciences. It discusses the underlying theory that supports symmetry studies by explaining the background of the symmetry studies in physics. It also demonstrates the usefulness of a unified view of algebra and symmetry studies to address data-analytic questions in optics. Computational tools and various examples from diverse areas of optical science are included, as is a brief review of finite group theory and distribution, quadratic forms, and elements of multivariate analysis.