  Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we
develop a cohomology theory of Rota-Baxter systems and justify it by
interpreting the lower degree cohomology groups as formal deformations and as
abelian extensions of Rota-Baxter systems. A further study on an
$L_\infty$-algebra structure associated to this cohomology theory will be given
in a subsequent paper.
