Commencing with a self-contained overview of atomic collision theory, this monograph presents recent developments of R-matrix theory and its applications to a wide-range of atomic molecular and optical processes. These developments include the electron and photon collisions with atoms, ions and molecules which are required in the analysis of laboratory and astrophysical plasmas, multiphoton processes required in the analysis of superintense laser interactions with atoms and molecules and positron collisions with atoms and molecules required in antimatter studies of scientific and technologial importance. Basic mathematical results and general and widely used R-matrix computer programs are summarized in the appendices.