In a preprint from 1982, John Milnor formulated various fundamental questions concerning infinite-dimensional Lie groups. In this paper, we describe some of the answers (and partial answers) obtained in the preceding years.
Helge Glökner. "Fundamental Problems in the Theory of Infinite-Dimensional Lie Groups." J. Geom. Symmetry Phys. 5 24 - 35, 2006. https://doi.org/10.7546/jgsp-5-2006-24-35