We present high resolution (R = 18,000), high signal-to-noise, 2 micron spectra of 52 infrared-selected Class I and flat-spectrum young stellar objects in the Taurus-Auriga, $rho$ Ophiuchi, Serpens, Perseus, and Corona Australis dark clouds. We detect key absorption lines in 41 objects and fit synthetic spectra generated from pre-main sequence models to deduce the effective temperatures, surface gravities, near-infrared veilings, rotation velocities, and radial velocities of each of these 41 sources. We find these objects to span ranges in effective temperature, surface gravity, and stellar luminosity which appear similar to those of late spectral-type Class II sources and classical T-Tauri stars. We determine that the mean 2 micron veiling of Class I and flat-spectrum objects is significantly higher than that of Class II objects in the same region where both types of objects are extensively observed ($rho$ Oph). We find a significant fraction of our protostellar sample also exhibits emission lines. Twenty-three objects show H$_2$ emission, usually indicative of the presence of energetic outflows. Thirty-four sources show HI Br $gamma$ emission and a number of these exhibit profile asymmetries consistent with in-fall. Eight sources show significant $Delta v = 2$ CO emission suggestive of emission from a circumstellar disk. Overall, these observations indicate that Class I and flat-spectrum objects are self-embedded protostars undergoing significant mass accretion, although the objects appear to span a broad range of mass accretion activity.
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