This research monograph is devoted to the geometry and topology of 3-dimensional manifolds (or, more generally, 3-dimensional orbifolds). This field was enormously influenced and advanced by work of W. Thurston, and the authors give a full proof of the Thurston orbifold theorem in the case where all local isotropy groups are cyclic subgroups of SO(3). As a consequence, they can prove the Thurston geometrisation conjecture for compact orientable irreducible 3-manifolds with a non-free symmetry. The first appendix is written in collaboration with M. Heusner.

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