  The fermion spectrum in the Standard Model (SM) exhibits hierarchical
structures between the eigenvalues of the Yukawa matrices which determine the
fermion masses, as well as certain hierarchical patterns in the mixing matrix
that describes weak transitions between different fermion generations. A
basis-independent description of the SM flavour structure can be given in terms
of a complete set of flavour invariants. In this paper, we construct a
convenient set of such invariants, and discuss the general form of the
renormalization-group equations. We also discuss the simplifications that arise
from exploiting hierarchies in Yukwawa couplings and mixings which are present
in the SM or its minimal-flavour violating extensions.
