The aim of this work is to provide a consistent and systematic treatment of the topological structure of 3-dimensional manifolds. Our ultimate goal
would be to provide (as have been done in dimension two) a "list"
containing exactly one 3-manifold from each homeomorphism class together
with an effective procedure for determining where a "given" 3-manifold
belongs in this list. While this problem remains far from solution, the
period since Papakyriakopoulos ' proofs of Dehn's lemma and the loop and
sphere theorems has produced considerable progress toward a solution and
we have attempted to provide an organized account of these developments.
We have excluded two topics: knot theory — which is a subject in itself
and for which there are several reference works ([10], [16], [75]) and a
consideration of local problems (wild embeddings, etc.) which are nicely
covered in [13].