Scattering theory is of interest to physicists and to chemists and has a wide variety of applications, but it also presents a considerable challenge to mathematicians, including numerical analysts. Within the Schr?dinger picture in this volume are collected the various theoretical and mathematical treatments of scattering together with a host of reviews of its applications to atomic and nuclear physics, to surface physics and chemistry, for example trapping of atoms on surfaces, and to amorphous condensed systems. The reviews give a concise and pedagogically useful presentation of the state of the art, and may serve as introductions for newcomers, in particular for graduate students.