X-ray absorption fine structure (XAFS) is a specific structure observed in X-ray absorption spectroscopy (XAS). By analyzing the XAFS, information can be acquired on the local structure and on the unoccupied local electronic states. Atomic spectra The atomic X-ray absorption spectrum (XAS) of a core-level in an absorbing atom is separated into states in the discrete part of the spectrum called "bounds final states" or "Rydberg states" below the ionization potential (IP) and "states in the continuum" part of the spectrum above the ionization potential due to excitations of the photoelectron in the vacuum. Above the IP the absorption cross section attenuates gradually with the X-ray energy. Following early experimental and theoretical works in the thirties, in the sixties using synchrotron radiation at the National Bureau of Standards it was established that the broad asymmetric absorption peaks are due to Fano resonances above the atomic ionization potential where the final states are many body quasi-bound states (i.e., a doubly excited atom) degenerate with the continuum. Spectra of molecules and condensed matter The XAS spectra of condensed matter are usually divided in three energy regions: Edge region The edge region usually extends in a range of few eV around the absorption edge. The spectral features in the edge region i) in good metals are excitations to final delocalized states above the Fermi level; ii) in insulators are core excitons below the ionization potential; iii) in molecules are electronic transitions to the first unoccupied molecular levels above the chemical potential in the initial states which are shifted into the discrete part of the core absorption spectrum by the Coulomb interaction with the core hole. Multi-electron excitations and configuration interaction between many body final states dominate the edge region in strongly correlated metals and insulators. For many years the edge region was referred to as the “Kossel structure” but now it is known as "absorption edge region" since the Kossel structure refers only to unoccupied molecular final states which is a correct description only for few particular cases: molecules and strongly disordered systems. X-ray Absorption Near Edge Structure The XANES energy region extends between the edge region and the EXAFS region over a 50-100 eV energy range around the core level x-ray absorption threshold. Before 1980 the XANES region was wrongly assigned to different final states: a) unoccupied total density of states, or b) unoccupied molecular orbitals (kossel structure) or c) unoccupied atomic