Summary: We study geometric and spectral properties of typical hyperbolic surfaces of high genus, excluding a set of small measure for the Weil-Petersson probability measure. We first prove Benjamini-Schramm convergence to the hyperbolic plane \(\mathcal{H}\) as the genus \(g\) goes to infinity. An estimate for the number of eigenvalues in an interval \([a,b]\) in terms of \(a,b\) and \(g\) is then proved using the Selberg trace formula. It implies the convergence of spectral measures to the spectral measure of \(\mathcal{H}\) as \(g\rightarrow+\infty\) and a uniform Weyl law as \(b\rightarrow +\infty\). We deduce a bound on the number of small eigenvalues and the multiplicity of any eigenvalue.