This is a proceedings paper of the RIMS workshop on ''Representation Theory and Analysis on Homogeneous Spaces'' held in Kyoto on 21-24 August 2006. We discuss the notions of 'stability' and 'local rigidity' of discontinuous groups with emphasis on non-Riemannian cases. Examples range from nilpotent, solvable, Riemannian, and pseudo-Riemannian symmetric spaces. In particular, structural results on the deformation space of discontinuous groups for semisimple group manifolds (as pseudo-Riemannian symmetric spaces) are explained, generalizing results of Kulkarni, Raymond, and Goldman.
© Toshiyuki Kobayashi