DescriptionA Ricci limit space (X, p) is the Gromov-Hausdorff limit of a sequence of complete n-manifolds (M_i, p_i) with Ric ≥ −(n − 1). We first study equivariant Gromov-Hausdorff convergence and consider closed isometric limit pseudo-group actions on a closed ball in a Ricci limit space. In particular, we establish a slice theorem for closed isometricpseudo-group actions on a closed ball. Using this slice theorem, we further study local fundamental groups of a Ricci limit space. We can show that for any ϵ > 0 and x ∈ X, there exists r < ϵ, depending on ϵ and x, so that any loop in B_r(x) is contractible in B_ϵ(x). In particular, X is semi-locally simply connected. As an application, we prove that the generalized Margulis lemma holds for Ricci limit spaces of n-manifolds.