  We construct a resonant normal form for an area-preserving map near a generic
resonant elliptic fixed point. The normal form is obtained by a simplification
of a formal interpolating Hamiltonian. The resonant normal form is unique and
therefore provides the formal local classification for area-preserving maps
with the elliptic fixed point. The total number of formal invariants is
infinite. We consider the cases of weak (of order $n\ge5$) and strong (of order
$n=3,4$) resonances. We also construct unique normal forms for analytic
families of area-preserving maps.
  We note that our constructions involve non-linear grading functions.
