Nevanlinna-Pick interpolation for time-varying input-output maps: The discrete case -- 0. Introduction -- 1. Preliminaries -- 2. J-Unitary operators on ?2 -- 3. Time-varying Nevanlinna-Pick interpolation -- 4. Solution of the time-varying tangential Nevanlinna-Pick interpolation problem -- 5. An illustrative example -- References -- Nevanlinna-Pick interpolation for time-varying input-output maps: The continuous time case -- 0. Introduction -- 1. Generalized point evaluation -- 2. Bounded input-output maps -- 3. Residue calculus and diagonal expansion -- 4. J-unitary and J-inner operators -- 5. Time-varying Nevanlinna-Pick interpolation -- 6. An example -- References -- Dichotomy of systems and invertibility of linear ordinary differential operators -- 1. Introduction -- 2. Preliminaries -- 3. Invertibility of differential operators on the real line -- 4. Relations between operators on the full line and half line -- 5. Fredholm properties of differential operators on a half line -- 6. Fredholm properties of differential operators on a full line -- 7. Exponentially dichotomous operators -- 8. References -- Inertia theorems for block weighted shifts and applications -- 1. Introduction -- 2. One sided block weighted shifts -- 3. Dichotomies for left systems and two sided systems -- 4. Two sided block weighted shifts -- 5. Asymptotic inertia -- 6. References -- Interpolation for upper triangular operators -- 1. Introduction -- 2. Preliminaries -- 3. Colligations & characteristic functions -- 4. Towards interpolation -- 5. Explicit formulas for ? -- 6. Admissibility and more on general interpolation -- 7. Nevanlinna-Pick Interpolation -- 8. Carathรฉodory-Fejรฉr interpolation -- 9. Mixed interpolation problems -- 10. Examples -- 11. Block Toeplitz & some implications -- 12. Varying coordinate spaces -- 13. References -- Minimality and realization of discrete time-varying systems -- 1. Preliminaries -- 2. Observability and reachability -- 3. Minimality for time-varying systems -- 4. Proofs of the minimality theorems -- 5. Realizations of infinite lower triangular matrices -- 6. The class of systems with constant state space dimension -- 7. Minimality and realization for periodical systems -- References