  In this paper, we elaborate Gr\"obner-Shirshov bases method for Leibniz
(super)algebras. We show that there is a unique reduced Gr\"obner-Shirshov
basis for every (graded) ideal of a free Leibniz (super)algebra. As
applications, we construct linear bases of free metabelian Leibniz
superalgebras and new linear bases of free metabelian Lie algebras. We present
a complete characterization of extensions of a Leibniz (super)algebra by
another Leibniz (super)algebra, where the former is presented by generators and
relations.

Rings and Algebras