IntroductionMany-body and correlation effects in solid-state physics manifest in specific signatures of the electronic band structure. The interaction of electrons with elementary excitations of the solid results in renormalization of the single-particle band structure due to, for example, electron-phonon, electron-magnon, and electron-electron interactions. This is explained in more detail in Volume 2 (Chapter 2) and this volume (Chapter 8). In particular for highly correlated materials such as charge (or spin) density wave materials, Mott insulators, and superconductors, such many-body effects are key to understanding macroscopic properties, for example, the electrical conductivity. Due to competition of these correlations with thermal fluctuations, phase transitions to ordered ground states with broken symmetry occur with decreasing temperature. Below the respective critical temperatures, the electronic system gains stability by opening of a bandgap (see Volume 2, Chapter 1). Understanding these many-particle effects is one goal of present efforts in solid-state physics.From an experimental point of view, angle-resolved photoelectron spectroscopy (ARPES) is the method of choice to analyze the electronic band structure of a solid [1,2]. It retrieves the information on the electronic states from the energy and the momentum of the photoelectrons emitted by a monochromatic photon source (see Volume 2, Chapter 3). This conversion is possible because the kinetic energy of the photoelectron is related to the binding energy of the photohole left behind. Furthermore, the translational symmetry of the surface guaranties that the momentum component of the photoelectron and of the photohole parallel to the surface are identical. However, the photoelectron wave vector perpendicular to the surface is not conserved due to the photoemission process. This limitation can be overcome if the material has a quasi-two-dimensional band structure. In this case, the angle-dependent photoelectron intensity represents the spectral function A k ðvÞ multiplied by the Fermi-Dirac distribution f ðvÞ.