This book will introduce advanced concepts and topics of solid-state theory. To this end we need a tool box that enables us to treat electron-electron interactions, and possibly also electron-phonon or phonon-phonon interactions in some well-defined, approximate way. The most advanced, yet still feasible approach, is the Green's function technique and the perturbation expansion using Feynman diagrams. This technique allows the interacting system to be treated as 'solid' within well-characterizable approximations, still widely used today, but also provides the language used in modern computer-based simulations as well as for the interpretation of experiments.