2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100853An extended version of a series of lectures given at Bogota in december 2002. It consists in a presentation of some aspects of Connes' and Kreimer's work on renormalization in the context of general connected Hopf algebras, in particular Birkhoff decomposition and, in the graded case, the scattering-type formula.Minor corrections, BCH approach precised in subsection II.6, references added. plain TeX, 6 eps figures, some xypic diagramsQuantum AlgebraHigh Energy Physics - TheoryCombinatorics16W30; 81R50text