  We extend results related to maximal subalgebras and ideals from Lie to
Leibniz algebras. In particular, we classify minimal non-elementary Leibniz
algebras and Leibniz algebras with a unique maximal ideal. In both cases, there
are types of these algebras with no Lie algebra analogue. We also give a
classification of E-Leibniz algebras which is very similiar to its Lie algebra
counterpart.
