This chapter is devoted to the theory of infinite-dimensional representations. For a G-manifold X with a proper and transitive action by a reductive subgroup L, there is a natural L-equivariant fiber bundle structure for X over the Riemannian symmetric space Y associated with L, with a compact fiber F. Consequently, the G-modules on the space of sections on G and the L-modules on the spaces of sections for L-equivariant vector bundles over Y are interconnected. This connection is defined by pull-back and push-forward operations involving integration along the compact fiber. However, the relationship between the following two aspects is not tightly linked in general from a spectral analysis perspective: We establish a sufficient condition for the G-module generated by any irreducible L-submodules in \(\mathcal{D}^{\prime}(X)\) to be finitely generated. Furthermore we establish a sufficient condition for the restriction of any irreducible G-modules in \(\mathcal{D}^{\prime}(X)\) to be discretely decomposable when restricted to the subgroup L. The existence problem of discrete series representations for some nonsymmetric spaces is also addressed as an application.