  Mixed functions are analytic functions in variables $z_1,..., z_n$ and their
conjugates $\bar z_1,..., \bar z_n$. We introduce the notion of Newton
non-degeneracy for mixed functions and develop a basic tool for the study of
mixed hypersurface singularities. We show the existence of a canonical
resolution of the singularity, and the existence of the Milnor fibration under
the strong non-degeneracy condition.
