2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67990This is survey about the classical knot concordance group, prepared for an upcoming handbook of knot theory. Topics include: the basic definitions of concordance; the theory of algebraic concordance as developed by Levine; the theory of Casson-Gordon invariants; applications of topological surgery as developed by Freedman; smooth results based on differential geometric techniques such as those of Donaldson; the filtration of the concordance group as developed by Cochran, Orr, and Teichner; and relations to classical 3-dimensional knot theory. There is also a short problem list.25 pages, 2 figures. Minor typographical changesGeometric Topology57M25text