Although the basic mathematical definition of a group and much of the abstract algebraic machinery applies to finite, infinite, and continuous groups, our interest for applications in nuclear engineering is limited to finite point groups. Furthermore, it should be kept in mind that most of the necessary properties of the crystallographic point groups for applications, such as the group multiplication tables, the class structures, irreducible representations, and characters are tabulated in reference books or can be obtained with modern software such as MAPLE or MATHEMATICA for example.