2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137134This is a selection of open problems dealing with ``large'' (non locally compact) topological groups and concerning extreme amenability (fixed point on compacta property), oscillation stability, universal minimal flows and other aspects of universality, and unitary representations.11 pages, LaTeX with macros, an invited contribution to the second edition of Open Problems In Topology (Elliott Pearl, editor), to be published by Elsevier Science in 2007. Comparing to version 2: comments on question 2 expanded, comments on recent developments around questions 17 and 18, a new question inserted between questions 40 and 41, and "forty" in the title became "forty-plus"General Topology22A05; 43A05; 43A07; 54H15text