Some Results from Scattering Theory --; Bound States Eigenfunction Expansions --; The Gel'fand-Levitan-Jost-Kohn Method --; Applications of Gel'fand --; Levitan Equation --; The Marchenko Method --; Examples --; Special Classes of Potentials --; Nonlocal Separable Interactions --; Miscellaneous Approaches to the Inverse Problems at Fixed l --; Scattering Amplitudes from Elastic Cross Sections --; Potentials from the Scattering Amplitude at Fixed Energy: General Equation and Mathematical Tools --; Potentials from the Scattering Amplitude at Fixed Energy: Matrix Methods --; Potentials from the Scattering Amplitude at Fixed Energy: Operator Methods --; The Three-Dimensional Inverse Problem --; Miscellaneous Approaches to Inverse Problems at Fixed Energy --; Approximate Methods --; Inverse Problems in One Dimension.