  We introduce the "Bluedisk" project, a large program at the Westerbork
Synthesis Radio Telescope (WSRT) that has mapped the HI in a sample of 23
nearby galaxies with unusually high HI mass fractions, along with a
similar-sized sample of control galaxies matched in stellar mass, size,
inclination and redshift. This paper presents the sample selection,
observational set-up, data reduction strategy, and a first analysis of the
sizes and structural properties of the HI disks. We find that the HI-rich
galaxies lie on the same HI mass versus HI size relation as normal spiral
galaxies, extending it to total HI masses of $2 \times 10^{10} M_{\odot}$ and
radii R1 of $\sim 100$ kpc (where R1 is defined as the radius where the HI
column density reaches 1 $M_{\odot}$ pc$^{-2}$). HI-rich galaxies have
significantly larger values of HI-to-optical size ratio at fixed stellar mass,
concentration index, stellar and star formation rate surface density compared
to the control sample. The disks of HI-rich galaxies are also significantly
more clumpy (i.e. have higher HI Gini and $\Delta$Area coefficient) than those
of normal spirals. There is no evidence that the disks of HI-rich galaxies are
more disturbed: HI-rich galaxies exhibit no difference with respect to control
samples in their distributions of HI asymmetry indices or optical/HI disk
position angle differences. In fact, the center of the HI distribution
corresponds more closely with the center of the optical light in the HI-rich
galaxies than in the controls. All these results argue against a scenario in
which new gas has been brought in by mergers. It is possible that they may be
more consistent with cooling from a surrounding quasi-static halo of warm/hot
gas.
