I will discuss: 1. discontinuous groups $\Gamma$ for symmetric spaces $X$ with indefinite metric and 2. spectral analysis of the Laplacian on $X/\Gamma$. In this situation, the Laplacian is no more an elliptic operator. Taking odd-dimensional anti- de Sitter manifolds as an example, I plan to illustrate some applications of Chern's ideas to the new construction of L2 spectrum which is stable under the deformation of discontinuous groups.