Mathematical Introduction Acoustic Phonons Plasmons, Optical Phonons, and Polarization Waves Magnons Fermion Fields and the Hartree-Fock Approximation Many-body Techniques and the Electron Gas Polarons and the Electron-phonon Interaction Superconductivity Bloch Functions - General Properties Brillouin Zones and Crystal Symmetry Dynamics of Electrons in a Magnetic Field: de Haas-van Alphen Effect and Cyclotron Resonance Magnetoresistance Calculation of Energy Bands and Fermi Surfaces Semiconductor Crystals I: Energy Bands, Cyclotron Resonance, and Impurity States Semiconductor Crystals II: Optical Absorption and Excitons Electrodynamics of Metals Acoustic Attenuation in Metals Theory of Alloys Correlation Functions and Neutron Diffraction by Crystals Recoilless Emission Green's Functions - Application to Solid State Physics Appendix: Perturbation Theory and the Electron Gas Index.