  The non-commutative analytic Toeplitz algebra is the weak operator topology
closed algebra generated by the left regular representation of the free
semigroup on $n$ generators. The structure theory of contractions in these
algebras is examined. Each is shown to have an $H^\infty$ functional calculus.
The isometries defined by words are shown to factor only as the words do over
the unit ball of the algebra. This turns out to be false over the full algebra.
The natural identification of weakly closed left ideals with invariant
subspaces of the algebra is shown to hold only for a proper subcollection of
the subspaces.
