2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99791The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some cases completely computable, in a way not possible with the traditional Postnikov systems, or with other models, such as simplicial groups.27 pages, uses xypic This paper is an edited version in LaTeX of the paper of the same title which appeared in the Adams Memorial Symposium on Algebraic Topology}, Vol 1, edited N. Ray and G Walker, Cambridge University Press, 1992, 187-210 version 2, August 13,2006: a number of minor corrections and improvements to the referencesAlgebraic Topology55P15, 55R35, 20L05text