  A subspace H of a Leibniz algebra L is called a quasi-ideal if [H;K] + [K;H]
\subseteq H + K for every subspace K of L. They include ideals and subalgebras
of codimension one in L. Quasi-ideals of Lie algebras were classified in two
remarkable papers of Amayo. The objective here is to extend those results to
the larger class of Leibniz algebras, and to classify those Leibniz algebras in
which every subalgebra is a quasi-ideal.
