  We present the mid-infrared (MIR) spectra obtained with the Spitzer InfraRed
Spectrograph (IRS) for a sample of 52 sources, selected as infrared luminous,
z>1 candidates in the Extragalactic First Look Survey (XFLS). The sample
selection criteria are f(24um) > 0.9mJy, nu fnu(24um)/nu fnu(8um) > 3.16 and nu
fnu(24um)/nu fnu(0.7um) > 10. Of the 52 spectra, 47 (90%) produced measurable
redshifts based solely on the mid-IR spectral features, with the majority
(35/47=74%) at 1.5<z<3.2. Keck spectroscopy of a sub-sample (17/47) agrees with
the mid-IR redshift measurements. The observed spectra fall crudely into three
categories -- (1) 33% (17/52) have strong PAH emission, and are probably
powered by star formation with total IR luminosity roughly a factor of 5 higher
than the local starburst ULIRGs. (2) 33% (17/52) have only deep silicate
absorption at 9.8um, indicative of deeply embedded dusty systems. The energetic
nature of the heating sources in these systems can not be determined by these
data alone. (3) The remainder 34% are mid-IR continuum dominated systems with
either weak PAH emission and/or silicate absorption. This third of the sample
are probably AGNs. From the silicate absorption feature, we estimate that
roughly two-thirds of the sample have optical depth tau(9.8um) > 1. Their
$L_{1600\AA}$ and $L_{\rm IR}$ suggest that our sample is among the most
luminous and most dust enshrouded systems of its epoch . Our study has revealed
a significant population of dust enshrouded galaxies at z~2, whose enormous
energy output, comparable to that of quasars, is generated by AGN as well as
starburst. This IR luminous population has very little overlap with sub-mm and
UV-selected populations (Abridged).
