  This 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.
