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 $200 - 671mu$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.}
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