We present a catalog of mid-infrared (MIR) spectra of 150 infrared (IR) luminous galaxies in the Spitzer extragalactic first look survey obtained with IRS on board Spitzer. The sample is selected to be brighter than ~0.9 mJy at 24 micron and it has a z distribution in the range [0.3,3.5] with a peak at z=1. It primarily comprises ultraluminous IR galaxies at z>1 and luminous IR galaxies at z<1, as estimated from their monochromatic 14 micron luminosities. The number of sources with spectra that are dominated by an active galactic nucleus (AGN) continuum is 49, while 39 sources have strong, star-formation related features. For this classification, we used the equivalent width (EW) of the 11.3 micron polycyclic aromatic hydrocarbon (PAH) feature. Several intermediate/high z starbursts have higher PAH EW than local ULIRGs. An increase in the AGN activity is observed with increasing z and luminosity, based on the decreasing EW of PAHs and the increasing [NeIII]/[NeII] ratio. Spectral stacking leads to the detection of the 3.3 micron PAH, the H2 0-0 S(1) and S(3) lines, and the [NeV] line. We observe differences in the flux ratios of PAHs in the stacked spectra of IR-luminous galaxies with z or luminosity, which are not due to extinction effects. When placing the observed galaxies on IR color-color diagrams, we find that the wedge defining AGN comprises most sources with continuum-dominated spectra, but also contains many starbursts. The comparison of the 11.3 micron PAH EW and the H-band effective radius, measured from HST data, indicates that sources with EW>2 micron, are typically more extended than ~3 kpc. However, there is no strong correlation between the MIR spectral type and the near-IR extent of the sources. [Abridged].
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