In developing the quantum chemical formalisms for chiroptical spectroscopy, one cannot avoid the involved mathematical expressions. This chapter, as it deals with one of the most mathematically intense topics, may not be palatable for those with limited mathematical background. Nevertheless, derivations are provided in greater detail, so that beginning researchers willing to explore can follow them with ease. Much of the quantum chemical formulation presented in this chapter is based on the lecture notes that the author has prepared (Polavarapu 1998) for a quantum chemistry course, taught at Vanderbilt University, drawn from the popular textbooks (Atkins 1983; Levine 1975). Those who do not want to wade through a multitude of expressions may skip to the end of the chapter where a summary is provided.