A theory whose objective is to determine the scattering object, or an interaction potential energy, from the knowledge of a scattered field. This is the opposite problem from direct scattering theory, where the scattering amplitude is determined from the equations of motion, including the potential. The equations of motion are usually linear (operator-valued) equations. An example of an inverse problem was given in an article by M. Kac entitled “Can One Hear the Shape of a Drum?” For some drums this question can be answered yes, for yet others no, but for many the question remains unanswered.