2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74904We compute the fundamental groups of non-singular analytic Deligne-Mumford curves, classify the simply connected ones, and classify analytic Deligne-Mumford curves by their uniformization type. As a result, we find an explicit presentation of an arbitrary Deligne-Mumford curve as a quotient stack. Along the way, we compute the automorphism 2-groups of weighted projective stacks $\mathcal{P}(n_1,n_2,...,n_r)$. We also discuss connections with the theory of F-groups, 2-groups, and Bass-Serre theory of graphs of groups.39 pages, 2 figuresAlgebraic Geometry14A20, 14H30, 30F10, 30F20text