Table of contents : 1. Semi-simplicial complexes - Appendix A - Appendix B: Definition of Homotopy Groups by Mappings of Spheres - Appendix C: Proof of the Hurewicz theorem The realization of a semi-simplicial complex 2. Monoid Complexes and Production of semi-simplicial complexes - Appendix A: Abelian Group Complexes The Construction FK 3. Acyclic Models 4. Spectral Sequences 5. DGA Algebras & the Construction of Cartan