Inverse scattering problems in quantum theory, Scattering theory of linear operators, rational matrix functions analytic and invertible on the unit circle, inverse problem in the Wiener algebra, Linear difference operators, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), second order difference block operator, orthonormal polynomials, realizations of the spectral or scattering function, Appell, Horn and Lauricella functions, scattering matrix function, spectral matrix function, Riesz projections, inverse spectral problem, Linear operator methods in interpolation, moment and extension problems, Schur coefficients