  Omega Centauri ($\omega$ Cen) is the most massive globular cluster of the
Milky Way. It is thought to be the nucleus of an accreted dwarf galaxy because
of its high mass and its complex stellar populations. To decipher its formation
history and study its dynamics, we created the most comprehensive kinematic
catalog for its inner region, by analyzing both archival and new Hubble Space
Telescope (HST) data. Our catalog contains 1 395 781 proper-motion measurements
out to the half-light radius of the cluster ($\sim$5.0') and down to
$m_{F625W}\approx$25. The typical baseline for our proper-motion measurements
is 20 years, leading to a median 1D proper motion precision of $\sim$11 $\mu$as
yr$^{-1}$ for stars with $m_{F625W}\approx$18 mag, with even better precision
($\sim$6.6 $\mu$as yr$^{-1}$) achieved in the extensively observed centermost
(r$<$1.5') region. In addition to our astrometric measurements, we also
obtained precise HST photometry in seven filters spanning from the ultraviolet
to the near-infrared. This allows detailed color-magnitude-diagram studies and
to separate the multiple stellar populations of the cluster. In this work, we
describe the data reduction used to obtain both the photometric and the
proper-motion measurements. We also illustrate the creation and the content of
our catalog, which is made publicly available. Finally, we present measurements
of the plane-of-sky rotation of $\omega$ Cen in the previously unprobed inner
few arcminutes and a precise measurement of the inclination $i =
(43.9\pm1.3)^\circ$.
