The basic physical principles of X-ray Absorption Fine-Structure (XAFS) are presented. XAFS is an element-specific spectroscopy in which measurements are made by tuning the X-ray energy at and above a selected core-level binding energy of a specified element. Although XAFS is a well-established technique providing reliable and useful information about the chemical and physical environment of the probe atom, its requirement of an energy-tunable X-ray source means it is primarily done with synchrotron radiation sources and so is somewhat less common than other spectroscopic analytical methods. XAFS spectra are especially sensitive to the oxidation state and coordination chemistry of the selected element. In addition, the extended oscillations of the XAFS spectra are sensitive to the distances, coordination number and species of the atoms immediately surrounding the selected element. This Extended X-ray Absorption Fine-Structure (EXAFS) is the main focus of this chapter. As it is element-specific, XAFS places few restrictions on the form of the sample, and can be used in a variety of systems and bulk physical environments, including crystals, glasses, liquids, and heterogeneous mixtures. Additionally, XAFS can often be done on low-concentration elements (typically down to a few ppm), and so has applications in a wide range of scientific fields, including chemistry, biology, catalysis research, material science, environmental science, and geology. Special attention in this chapter is given to the basic concepts used in analysis and modeling of EXAFS spectra. X-ray absorption fine structure (XAFS) is the modulation of an atom’s X-ray absorption probability at energies near and above the binding energy of a core-level electron of the atom. The XAFS is due to the chemical and physical state of the absorbing atom. XAFS spectra are especially sensitive to the formal oxidation state, coordination chemistry, and the distances, coordination number and species of the atoms immediately surrounding the selected …