Abstract: We shall first review the main known results concerning the analytic classification
of germs of codimension one singular holomorphic foliations, in dimension two and three.
We focus in the works from Cerveau, Moussu, Meziani, Berthier, Sad, Strozyna and others,
in the nilpotent case. The state-of-art of this subject in dimension three will be explained.
In particular, how the existence of a (pre)-normal form may be helpful, and which are some
of the techniques involved. This is included in several works in collaboration with Percy
Fernández and Hernán Neciosup (LIma, Perú).