| Résume||Nichols algebras play a crucial rôle in the classification of finite-dimensional complex pointed Hopf algebras in the context of Lifting method given by Andruskiewitsch and Schneider. These authors have obtained the classification when the group-likes form an abelian group whose order is relatively prime to 210 ('05).
This talk is based on a series of articles concerned with the non-abelian case. I will describe a strategy to approach the classification by means of Nichols algebras coming from a rack and a 2-cocycle. I will show some criteria to decide the dimension of these Nichols algebras and I will presented a list of the results obtained for some families of non-abelian groups.
 N. Andruskiewitsch, F. Fantino, M. Graña and L. Vendramin, ``Finite-dimensional pointed Hopf algebras with alternating groups are trivial'', Ann. Mat. Pura Appl. (4) 190 2 (2011) 225-245.
 N. Andruskiewitsch, F. Fantino, M. Graña and L. Vendramin, ``Pointed Hopf algebras over the sporadic simple groups'', J. Algebra 325 1 (2011) 305-320.
 F. Fantino and G. A. García, ``On pointed Hopf algebras over dihedral groups'', Pacific J. Math., 252 1 (2011), 69-91.|