  A Rota-Baxter Leibniz algebra is a Leibniz algebra
$(\mathfrak{g},[~,~]_{\mathfrak{g}})$ equipped with a Rota-Baxter operator $T :
\mathfrak{g} \rightarrow \mathfrak{g}$. We define representation and dual
representation of Rota-Baxter Leibniz algebras. Next, we define a cohomology
theory of Rota-Baxter Leibniz algebras. We also study the infinitesimal and
formal deformation theory of Rota-Baxter Leibniz algebras and show that our
cohomology is deformation cohomology. Moreover, We define an abelian extension
of Rota-Baxter Leibniz algebras and show that equivalence classes of such
extensions are related to the cohomology groups.
