  In this paper we give a complete classification of two-step nilpotent Leibniz
algebras in terms of Kronecker modules associated with pairs of bilinear forms.
In particular, we describe the complex and the real case of the indecomposable
Heisenberg Leibniz algebras as a generalization of the classical
$(2n+1)-$dimensional Heisenberg Lie algebra $\mathfrak{h}_{2n+1}$. Then we use
the Leibniz algebras - Lie local racks correspondence proposed by S. Covez to
show that nilpotent real Leibniz algebras have always a global integration. As
an application, we integrate the indecomposable nilpotent real Leibniz algebras
with one-dimensional commutator ideal. We also show that every Lie quandle
integrating a Leibniz algebra is induced by the conjugation of a Lie group and
the Leibniz algebra is the Lie algebra of that Lie group.
