The book describes the modern theory of light hydrogen-like systems, and the discussion is based on quantum electro-dynamics. In particular, Green's functions, relativistic bound-state equations and Feynman diagrams are extensively used. New theoretical approaches are described and explained. The book contains derivation of many theoretical results obtained in recent years. A complete set of all theoretical results for the energy levels of hydrogen-like bound states, as well as comparison with experiment, is presented.