I. Interaction of Light and Matter, The Raman Scattering Tensor.- I-1. Electromagnetic Radiation of an Oscillating Dipole.- I-2. Higher Order Moments: Quadrupoles and Magnetic Dipoles.- I-3. Spectroscopic Transitions.- I-4. Classical Considerations of the Radiation Field and Quantum Mechanical Calculation of the Induced Dipole Moment, the Correspondence Principle.- I-5. Formulation of the Scattering Tensor.- I-6. Symmetry of the Scattering Tensors.- II. Properties of Tensors.- II-1. Vectors and Dyadics.- II-2. Scattering Tensors and Radiation from Classical Oscillators.- II-3. Rotation of Tensors.- II-4. Specific Rotation of Symmetric and Antisymmetric Tensors.- III. Some Aspects of Group Theory.- III-1. Symmetry Elements.- III-2. Definition Properties of Point, Space and Factor Groups.- III-3. Representations of Groups.- III-4. Transformation Properties of the Scattering Tensor.- III-5. Irreducible Tensors and Their Transformation Properties.- III-6. The Scattering Operator.- IV. The Normal Raman Effect.- IV-1. Theory of the Electronic Raman Effect.- IV-2. Electronic Levels and Selection Rules.- IV-3. Normal Modes, Normal Coordinates and Vibrational Wave Functions.- IV-4. Theory of the Vibrational Raman Effect.- IV-5. The Case of Degenerate Electronic States.- IV-6. Rotational Levels and Wave Functions.- IV-7. The Rotational Raman Effect.- IV-8. Depolarization Ratios.- V. Other Scattering Processes.- V-l. The Hyper Raman Effect.- V-2. The Stimulated Raman Effect.- V-3. Induced Absorption: The Inverse Raman Effect.- V-4. The Resonance Raman Effect.- Appendix I. Properties of Representations of Some Important Point Groups.