1. Introduction 2. Preliminaries 3. Fundamental matrix inequalities 4. On $\mathcal {H}(\Theta)$ spaces 5. Parametrizations of all solutions 6. The equality case 7. Nontangential limits 8. The Nevanlinna-Pick boundary problem 9. A multiple analogue of the Carathéodory-Julia theorem 10. On the solvability of a Stein equation 11. Positive definite solutions of the Stein equation 12. A Carathéodory-Fejér boundary problem 13. The full matrix Carathéodory-Fejér boundary problem 14. The lossless inverse scattering problem
