For geometrically finite hyperbolic manifolds Γℍn+1, we prove the meromorphic extension of the resolvent of Laplacian, Poincaré series, Einsenstein series and scattering operator to the whole complex plane. We also deduce the asymptotics of lattice points of Γ in large balls of ℍn+1 in terms of the Hausdorff dimension of the limit set of Γ.