  The local invariants of a meromorphic Abelian differential on a Riemann
surface of genus $g$ are the orders of zeros and poles, and the residues at the
poles. The main result of this paper is that with few exceptions, every pattern
of orders and residues can be obtain by an Abelian differential. These
exceptions are two families in genus zero when the orders of the poles are
either all simple or all nonsimple. Moreover, we even show that the pattern can
be realized in each connected component of strata. Finally we give consequences
of these results in algebraic and flat geometry. The main ingredient of the
proof is the flat representation of the Abelian differentials.
