2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68361We give a brief survey of many of the high-lights of our present understanding of the young subject of quantum metric spaces, and of quantum Gromov-Hausdorff distance between them. We include examples.Intended for the proceedings of the AMS Special Session ``Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration in Honor of J. V. Neumann and M. H. Stone, II'', editors R. S. Doran and R. V. KadisonOperator AlgebrasMetric Geometry46L87 (Primary) 14E20, 53C23, 58B34 (Secondary)text