Suppose that $M$ is a closed Riemannian manifold: one can construct the so called Laplace-Beltrami operator on $M$. It's spectrum contains some information of the underlying manifold: for example it's dimension is encoded by the asymptotic behaviour of eigenvalues. As far as I know, there was a problem whether two isospectral closed manifolds are isometric-the negative answer was found by Milnor. So from this story I suspect that people believed that the spectrum of Laplacian will contain a lot of (geometric) information about the underlying manifold. My question is following:

Is is possible to extract the information about the fundamental group of $M$ from the spectrum of Laplace operator?