  We recall first some basic facts on weighted homogeneous functions and
filtrations in the ring $A$ of formal power series. We introduce next their
analogues for weighted homogeneous diffeomorphisms and vector fields. We show
that the Milnor algebra is a complete invariant for the classification of
weighted homogeneous polynomials with respect to right-equivalence, i.e. change
of coordinates in the source and target by diffeomorphism.
