Algebraic Theory of Molecules presents a fresh look at the mathematics of wave functions that provide the theoretical underpinnings of molecular spectroscopy. Written by renowned authorities in the field, the book demonstrates the advantages of algebraic theory over the more conventional geometric approach to developing the formal quantum mechanics inherent in molecular spectroscopy. Many examples are provided that compare the algebraic and geometric methods, illustrating the relationship between the algebraic approach and current experiments. The authors develop their presentation from a basic level so as to enable newcomers to enter the field while providing enough details and concrete examples to serve as a reference for the expert. Chemical physicists, physical chemists, and spectroscopists will want to read this exciting new approach to molecular spectroscopy. Read more... Content: Ch. 1. The Wave Mechanics of Diatomic Molecules — Ch. 2. Summary of Elements of Algebraic Theory — Ch. 3. Mechanics of Molecules — Ch. 4. Three-body Algebraic Theory — Ch. 5. Four-Body Algebraic Theory — Ch. 6. Many-Body Algebraic Theory — Ch. 7. Classical Limit and Coordinate Representation — Ch. 8. Prologue to the Future — Appendix A Properties of Lie Algebras — Appendix B Coupling of Algebras — Appendix C Hamiltonian Parameters. Abstract: Algebraic Theory of Molecules presents a fresh look at the mathematics of wave functions that provide the theoretical underpinnings of molecular spectroscopy. Written by renowned authorities in the field, the book demonstrates the advantages of algebraic theory over the more conventional geometric approach to developing the formal quantum mechanics inherent in molecular spectroscopy. Many examples are provided that compare the algebraic and geometric methods, illustrating the relationship between the algebraic approach and current experiments. The authors develop their presentation from a basic level so as to enable newcomers to enter the field while providing enough details and concrete examples to serve as a reference for the expert. Chemical physicists, physical chemists, and spectroscopists will want to read this exciting new approach to molecular spectroscopy