  The paper presents new high angular resolution ALMA 1.3 mm dust continuum
observations of the protoplanetary system AS 209 in the Ophiuchus star forming
region. The dust continuum emission is characterized by a main central core and
two prominent rings at $r = 75\,$au and $r = 130\,$au intervaled by two gaps at
at $r = 62\,$au and $r = 103\,$au. The two gaps have different widths and
depths, with the inner one being narrower and shallower. We determined the
surface density of the millimeter dust grains using the 3D radiative transfer
disk code \textsc{dali}. According to our fiducial model the inner gap is
partially filled with millimeter grains while the outer gap is largely devoid
of dust. The inferred surface density is compared to 3D hydrodynamical
simulations (FARGO-3D) of planet-disk interaction. The outer dust gap is
consistent with the presence of a giant planet ($M_{\rm planet} \sim
0.8\,M_{\rm Staturn}$); the planet is responsible for the gap opening and for
the pile-up of dust at the outer edge of the planet orbit. The simulations also
show that the same planet can give origin to the inner gap at $r = 62\,$au. The
relative position of the two dust gaps is close to the 2:1 resonance and we
have investigated the possibility of a second planet inside the inner gap. The
resulting surface density (including location, width and depth of the two dust
gaps) are in agreement with the observations. The properties of the inner gap
pose a strong constraint to the mass of the inner planet ($M_{\rm planet} <
0.1\,M_{\rm J}$). In both scenarios (single or pair of planets), the
hydrodynamical simulations suggest a very low disk viscosity ($\alpha <
10^{-4}$). Given the young age of the system (0.5 - 1 Myr), this result implies
that the formation of giant planets occurs on a timescale of $\lesssim$ 1\,Myr.
