This comprehensive text explores modern methods related to the nuclear shell, particularly in regard to the techniques of spectroscopy. Since a thorough grasp of these methods involves group theory, the authors make a point of developing a correspondence between these areas. Although a familiarity with group theory is not a prerequisite to the study of shell model methods, an acquaintance with the subject will facilitate understanding of the group theoretical meanings of ideas and formalism.Geared toward graduate students who have had a course in elementary quantum mechanics, this text explains the necessary additional formalism. Tensor algebra, the most important mathematical tool needed, is developed in detail in Part II. By keeping the mathematics as simple as possible and by emphasizing the physical content of the formalism, the authors have made this volume a valuable resource for experimentalists and theorists as well as students.