2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104735These notes are based on a series of five lectures given during the summer school ``Interactions between Homotopy Theory and Algebra'' held at the University of Chicago in 2004.39 pages. Final version for the Proceedings of the Summer School ``Interactions between Homotopy Theory and Algebra'' at Chicago in 2004K-Theory and HomologyCategory Theorytext