Review of scattering theory -- Derivation of the phase equation -- Discussion of the phase equation and of the behavior of the phase function : procedures for the numerical computation of scattering phase shifts -- Phase function, examples -- Connection between phase function and radial wave function : the amplitude function -- Bounds on the scattering phase shift and on its variation with energy -- Born approximation and improved Born approximation -- Variational and extremum principles for evaluationg scattering phase shifts -- Born approximation, improved Born approximation, variational and extremum principles -- Low-energy expansion, scattering length and effective range, bounds on the zero-energy cross section -- Scattering length and its approximate and variational expressions -- Scattering length and its approximate and variational expressions -- Generalized formulation of the phase method, other types of phase equations -- Simultaneous maximum and minimum principles for the evaluation of scattering phase shifts -- Scattering on singular potentials, high-energy behavior and approximate expression of the scattering phase shift in this case -- Further generalization of the phase method -- Scattering of Dirac particles -- Scattering on nonlocal potentials and on complex potentials -- Multichannel case -- Bound states, discussion of the pole equation and of the behavior of the pole functions for q> 0 -- Behavior of pole functions and computation of binding energies -- Relation between the number of bound states and the value of the scattering phase shift at zero energy (Levinson's theorem) -- Bounds on the number and energies of bound states in a given potential, necessary and sufficient conditions for the existence of bound states.