A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a
nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S.<BR>The construction is very explicit and uses techniques from resolution of
singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students.