  The differential cross sections and unpolarized spin-density matrix elements
for the reaction $\gamma p\to p\omega$ were measured using the CBELSA/TAPS
experiment for initial photon energies ranging from the reaction threshold to
2.5 GeV. These observables were measured from the radiative decay of the
$\omega$ meson, $\omega\to\pi^0\gamma$. The cross sections cover the full
angular range and show the full extent of the $t$-channel forward rise. The
overall shape of the angular distributions in the differential cross sections
and unpolarized spin-density matrix elements are in fair agreement with
previous data. In addition, for the first time, a beam of linearly-polarized
tagged photons in the energy range from 1150 MeV to 1650 MeV was used to
extract polarized spin-density matrix elements.
  These data were included in the Bonn-Gatchina partial wave analysis (PWA).
The dominant contribution to $\omega$ photoproduction near threshold was found
to be the $3/2^+$ partial wave, which is primarily due to the sub-threshold
$N(1720)\,3/2^+$ resonance. At higher energies, pomeron-exchange was found to
dominate whereas $\pi$-exchange remained small. These $t$-channel contributions
as well as further contributions from nucleon resonances were necessary to
describe the entire dataset: the $1/2^-$, $3/2^-$, and $5/2^+$ partial waves
were also found to contribute significantly.
