2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223857This is a survey on local dynamics of holomorphic maps in one and several complex variables, discussing in particular normal forms and the structure of local stable sets in the non-hyperbolic case, and including several proofs and a vast bibliography. It updates and enlarge the previous survey arXiv:math/0310089v1.Notes of the CIME course given in Cetraro (Italy) in July 2008. To appear in "Holomorphic dynamics", G.Gentili, J. Guenot, G. Patrizio eds., Lect. Notes in Math., Springer, Berlin, 2009Dynamical SystemsComplex Variables37F99 (Primary); 32H50, 30D05 (Secondary)text