Isometric and unitary dilations of a contraction operator Further properties of the minimal unitary dilation Characteristic function and function model Further comments on the characteristic function $\Phi_T(\lambda)$ Invariant subspaces and factorizations of the characteristic function Commutative systems Lifting of intertwining operators Functional calculus for a contraction Operators of class $C_0$ and the Jordan model Examples of quasi-similarity and the class $N_T$ of functions References.