  In this paper we begin to study the subalgebra lattice of a Leibniz algebra.
In particular, we deal with Leibniz algebras whose subalgebra lattice is
modular, upper semi-modular, lower semi-modular, distributive, or dually
atomistic. The fact that a non-Lie Leibniz algebra has fewer one-dimensional
subalgebras in general results in a number of lattice conditions being weaker
than in the Lie case.
