  We present the Herschel SPIRE Fourier Transform Spectroscopy (FTS) atlas for
a complete flux limited sample of local Ultra-Luminous Infra-Red Galaxies as
part of the HERschel ULIRG Survey (HERUS). The data reduction is described in
detail and was optimized for faint FTS sources with particular care being taken
with the subtraction of the background which dominates the continuum shape of
the spectra. Special treatment in the data reduction has been given to any
observation suffering from artefacts in the data caused by anomalous
instrumental effects to improve the final spectra. Complete spectra are shown
covering $200 - 671\mu$m with photometry in the SPIRE bands at 250$\mu$m,
350$\mu$m and 500$\mu$m. The spectra include near complete CO ladders for over
half of our sample, as well as fine structure lines from [CI] 370 $\mu$m, [CI]
609 $\mu$m, and [NII] 205 $\mu$m. We also detect H$_{2}$O lines in several
objects. We construct CO Spectral Line Energy Distributions (SLEDs) for the
sample, and compare their slopes with the far-infrared colours and
luminosities. We show that the CO SLEDs of ULIRGs can be broadly grouped into
three classes based on their excitation. We find that the mid-J (5$<$J$<$8)
lines are better correlated with the total far-infrared luminosity, suggesting
that the warm gas component is closely linked to recent star-formation. The
higher J transitions do not linearly correlate with the far-infrared
luminosity, consistent with them originating in hotter, denser gas unconnected
to the current star-formation. {\bf We conclude that in most cases more than
one temperature components are required to model the CO SLEDs.}
