  This is a survey on the local structure about a fixed point of discrete
finite-dimensional holomorphic dynamical systems, discussing in particular the
existence of local topological conjugacies to normal forms, and the structure
of local stable sets in the non-hyperbolic case. The author hopes to keep the
survey up to date, and thus it would be grateful to anybody pointing out
missing (or mistaken) results and references, and/or suggesting topics to be
included or expanded in it.
