The aim of this work is to classify foliations on CP 2 of degree 3 with degenerate singular points. For that we construct a stratification of the space of holomorphic foliations by locally closed, irreducible, non-singular algebraic subvarieties which parametrize foliations with a special degenerate singularity. We also prove that there are only two foliations with isolated singularities with automorphism group of dimension two, the maximum possible dimension. Finally we obtain the unstable foliations with only one singular point, that is, a singular point with Milnor number 13.