The subject of this monograph is nonrelativistic scattering on a spherically symmetrical potential. More specifically, the discussion is focused on the scattering phase shift b_l, which, for each value of the angular momentum l, represents all the effect of the potential that is relevant for the quantum mechanical description of elastic scattering. The treatment makes no attempt to go beyond the standards of mathematical rigor that are usually considered satisfactory in physics. In fact, whenever possible the emphasis is on the physical understanding rather than the mathematical formalism. It is nevertheless hoped that the number of imprecise or incorrect statements will be minimal.