Absorption spectroscopy provides information on the chemical nature, atomic structure and concentration of hydrogen-like centers, to which belong most of the dopants of semiconductors and insulators. In this book, an introduction to the bulk optical properties of these materials and to the properties of hydrogen-like centers is first provided, followed by a description of set-ups used in absorption spectroscopy. The results of the calculations of the energy levels of these centres by effective-mass theory are exposed. Detailed absorption data on specific classes of centres are compared with theory, and atomic structures are deduced from absorption measurements under external perturbations.