  Given a symmetric Leibniz algebra $(\mathcal{L},.)$, the product is
Lie-admissible and defines a Lie algebra bracket $[\;,\;]$ on $\mathcal{L}$.
Let $G$ be the connected and simply-connected Lie group associated to
$(\mathcal{L},[\;,\;])$. We endow $G$ with a Lie rack structure such that the
right Leibniz algebra induced on $T_eG$ is exactly $(\mathcal{L},.)$. The
obtained Lie rack is said to be associated to the symmetric Leibniz algebra
$(\mathcal{L},.)$. We classify symmetric Leibniz algebras in dimension 3 and 4
and we determine all the associated Lie racks. Some of such Lie racks give rise
to non-trivial topological quandles. We study some algebraic properties of
these quandles and we give a necessary and sufficient condition for {them} to
be quasi-trivial.
