Basic Operator Theory -- The Wold Decomposition -- Toeplitz and Laurent Operators -- Inner and Outer Functions -- Rational Inner and Outer Functions -- The Naimark Representation -- The Rational Case -- Finite Section Techniques -- The Levinson Algorithm and Factorization -- Isometric Representations and Factorization -- Signal Processing -- Riccati Methods -- Riccati Equations and Factorization -- Kalman and Wiener Filtering -- Interpolation Theory -- Tangential Nevanlinna-Pick Interpolation -- Contractive Nevanlinna-Pick Interpolation -- Appendices -- A Review of State Space -- The Levinson Algorithm.