Resolvent of the Laplacian on geometrically finite hyperbolic manifolds

For geometrically finite hyperbolic manifolds $\mathrm{\Gamma }\mathrm{\backslash }{H}^{n+1}$, we prove the meromorphic extension of the resolvent of Laplacian, Poincar'e series, Einsenstein series and scattering operator to the whole complex plane. We also deduce the asymptotics of lattice points of $\mathrm{\Gamma }$ in large balls of $H^{n+1}$ in terms of the Hausdorff dimension of the limit set of $\mathrm{\Gamma }$.