Nonabelian Algebraic Topology

This talk gave a sketch of the contents and background to a book with the title `Nonabelian algebraic topology’ being written under support of a Leverhulme Emeritus Fellowship (2002-2004) by the speaker and Rafael Sivera (Valencia). The aim is to give in one place a full account of work by R. Brown and P.J. Higgins since the 1970s which defines and applies crossed complexes and cubical higher homotopy groupoids in algebraic topology and group cohomology.