  We present an approach to Gromov-Witten invariants that works on arbitrary
(closed) symplectic manifolds. We avoid genericity arguments and take into
account singular curves in the very formulation. The method is by first
endowing mapping spaces from (prestable) algebraic curves into the symplectic
manifold with the structure of a Banach orbifold and then exhibiting the space
of stable $J$-curves (``stable maps'') as zero set of a Fredholm section of a
Banach orbibundle over this space. The invariants are constructed by pairing
with a homology class on the locally compact topological space of stable
$J$-curves that is generated as localized Euler class of the section.
