  In this paper we study canonical models for representations of the Hardy
algebras that generalize the model theory of Sz.-Nagy and Foias for contraction
operators.
  The Hardy algebras are non selfadjoint operator algebras associated with
$W^*$-correspondences. This class includes the classical $H^{\infty}$ algebra,
free semigroup algebras, quiver algebras and other classes of algebras studied
in the literature.
