  We classify isotopy classes of automorphisms (self-homeomorphisms) of
3-manifolds satisfying the Thurston Geometrization Conjecture. The
classification is similar to the classification of automorphisms of surfaces
developed by Nielsen and Thurston, except an automorphism of a reducible
manifold must first be written as a suitable composition of two automorphisms,
each of which fits into our classification. Given an automorphism, the goal is
to show, loosely speaking, either that it is periodic, or that it can be
decomposed on a surface invariant up to isotopy, or that it has a "dynamically
nice" representative, with invariant laminations that "fill" the manifold.
  We consider automorphisms of irreducible and boundary-irreducible 3-manifolds
as being already classified, though there are some exceptional manifolds for
which the automorphisms are not understood. Thus the paper is particularly
aimed at understanding automorphisms of reducible and/or boundary reducible
3-manifolds.
  Previously unknown phenomena are found even in the case of connected sums of
products of a 2-sphere with a 1-sphere. To deal with this case, we prove that a
minimal genus Heegaard decomposition is unique up to isotopy, a result which
apparently was previously unknown.
  Much remains to be understood about some of the automorphisms of the
classification.
