%$Modified: Mon Apr 28 14:56:21 2003 by wgd $

                     Localization

                     W. G. Dwyer

This is a largely expository paper, which describes the concept of
localization, as it usually comes up in topology, and gives some
examples of it. The examples include local homology and cohomology,
homological localizations of spaces and spectra, and localization with
respect to a map f. For appropriate choices of the map f, this last
gives constructions related to the Goodwillie calculus and to motivic
homotopy theory. There's also a proof that if a localization functor
exists, the higher order categorical invariants associated to
inverting the local equivalences are trivial.