Introduction An outline of the proof Notation Toroidal morphisms and prepared morphisms Toroidal ideals Toroidalization of morphisms from 3-folds to surfaces Preparation above 2 and 3-points Preparation The $\tau$ invariant Super parameters Good and perfect points Relations Well prepared morphisms Construction of $\tau$-well prepared diagrams Construction of a $\tau$-very well prepared morphism Toroidalization Proofs of the main results List of technical terms Bibliography.
