Two of the Original Papers -- New L2 Approach to Quantum Scattering: Theory -- J-Matrix Method: Extensions to Arbitrary Angular Momentum and to Coulomb Scattering -- Theoretical and Mathematical Considerations -- Oscillator Basis in the J-Matrix Method: Convergence of Expansions, Asymptotics of Expansion Coefficients and Boundary Conditions -- Scattering Phase Shift for Relativistic Separable Potentials with Laguerre-Type Form Factors -- Accurate Evaluation of the S-Matrix for Multi-Channel Analytic and Non-Analytic Potentials in Complex L2 Bases -- J-Matrix and Isolated States -- On the Regularization in J-Matrix Methods -- Applications in Atomic Physics -- The J-Matrix Method: A Universal Approach to Description of Ionization of Atoms -- J-Matrix Green’s Operators and Solving Faddeev Integral Equations for Coulombic Systems -- The Use of a Complex Scaling Method to Calculate Resonance Partial Widths -- Applications in Nuclear Physics -- J-Matrix Approach to Loosely-Bound Three-Body Nuclear Systems -- Nucleon–Nucleon Interaction in the J-Matrix Inverse Scattering Approach and Few-Nucleon Systems -- The Modified J-Matrix Approach for Cluster Descriptions of Light Nuclei -- Other Related Methods: Chemical Physics Application -- A Generalized Formulation of Density Functional Theory with Auxiliary Basis Sets.