  The Leibniz algebras appeared as a generalization of the Lie algebras. In
this work we deal with the classification of nilpotent complex Leibniz algebras
of low dimensions. Namely, the classification of nilpotent complex Leibniz
algebras dimensions less than 3 is extended to the dimension four. {\it AMS
Subject Classifications}: 16D70, 17A30, 17A60, 17B30 {\it Key words:} Leibniz
algebra, associative algebra, nilpotence, nulfiliform Leibniz algebra, filiform
Leibniz algebra.
