  We establish topological local rigidity for uniform lattices in compactly
generated groups, extending the result of Weil from the realm of Lie groups. We
generalize the classical local rigidity theorem of Selberg, Calabi and Weil to
irreducible uniform lattices in $\text{Isom}(X)$ where $X$ is a proper
$\text{CAT}(0)$ space with no Euclidian factors, not isometric to the
hyperbolic plane. We deduce an analog of Wang's finiteness theorem for certain
non-positively curved metric spaces.
