  We present a detailed analysis of the high-angular resolution (0.''037,
corresponding to 5 au) observations of the 1.25 mm continuum and $^{12}$CO
$2-1$ emission from the disk around the T Tauri star AS 209. AS 209 hosts one
of the most unusual disks from the DSHARP sample, the first high angular
resolution ALMA survey of disks (Andrews et al. 2018), as nearly all of the
emission can be explained with concentric Gaussian rings. In particular, the
dust emission consists of a series of narrow and closely spaced rings in the
inner $\sim$60 au, two well-separated bright rings in the outer disk, centered
at 74 and 120 au, and at least two fainter emission features at 90 and 130 au.
We model the visibilities with a parametric representation of the radial
surface brightness profile, consisting of a central core and 7 concentric
Gaussian rings. Recent hydro-dynamical simulations of low viscosity disks show
that super-Earth planets can produce the multiple gaps seen in AS 209
millimeter continuum emission. The $^{12}$CO line emission is centrally peaked
and extends out to $\sim$300 au, much farther than the millimeter dust
emission. We find axisymmetric, localized deficits of CO emission around four
distinct radii, near 45, 75, 120 and 210 au. The outermost gap is located well
beyond the edge of the millimeter dust emission, and therefore cannot be due to
dust opacity and must be caused by a genuine CO surface density reduction, due
either to chemical effects or depletion of the overall gas content.
