  We first present the construction of the moduli space of real
pseudo-holomorphic curves in a given real symplectic manifold. Then, following
the approach of Gromov and Witten, we construct invariants under deformation of
real rational symplectic 4-manifolds. These invariants provide lower bounds for
the number of real rational $J$-holomorphic curves in a given homology class
passing through a given real configuration of points.
