  Leibniz algebras are certain generalization of Lie algebras. In this paper we
give classification of non-Lie solvable (left) Leibniz algebras of dimension
$\leq 8$ with one dimensional derived subalgebra. We use the canonical forms
for the congruence classes of matrices of bilinear forms to obtain our result.
Our approach can easily be extended to classify these algebras of higher
dimensions. We also revisit the classification of three dimensional non-Lie
solvable (left) Leibniz algebras.

Rings and Algebras