Introduction 1. Function models for completely nonunitary contractions 2. Function models for unitary operators 3. Factorization and invariant subspaces 4. Operator nodes and characteristic functions 5. Factorization of nodes and invariant subspaces 6. Spectral invariants for $T_u$ 7. A perturbation problem: the operator $L = U(I-L_0)$ 8. Multiplicity theory for $U$ 9. Comparison of $U_{ac}$ with $L_u$ 10. Concluding remarks
