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General theory.- Essential singular surfaces in some special 3-manifolds.- Characteristic submanifolds.- Singular surfaces and characteristic submanifolds.- Singular submanifolds and characteristic submanifolds.- Invariance of the characteristic submanifolds under homotopy equivalences.- Simple 3-manifolds.- Attaching homotopy equivalences.- Dehn twists of 3-manifolds.- Dehn flips of 3-manifolds.- Homotopy equivalences of surfaces and I-bundles.- Geometric properties of 3-manifold groups.