Classification of Low Dimensional Nilpotent Leibniz algebras

In this paper we give all isomorphism classes of $4-$dimensional nilpotent Leibniz algebras by using modified of Skjelbred and Sund method. To classify four dimensional case we need the classification of two and three dimensional nilpotent Leibniz algebras. Throughout this paper $F$ is complex numbers field. We denote the $j-$th algebra of dimension $i$ by $L_{i,j}.$\\