We present fundamental parameters for 110 canonical K- & M-type (1.3$-$0.13$M_odot$) Taurus-Auriga young stellar objects (YSOs). The analysis produces a simultaneous determination of effective temperature ($T_{rm eff}$), surface gravity ($log$ g), magnetic field strength (B), and projected rotational velocity ($v sin i$). Our method employed synthetic spectra and high-resolution (R$sim$45,000) near-infrared spectra taken with the Immersion GRating INfrared Spectrometer (IGRINS) to fit specific K-band spectral regions most sensitive to those parameters. The use of these high-resolution spectra reduces the influence of distance uncertainties, reddening, and non-photospheric continuum emission on the parameter determinations. The median total (fit + systematic) uncertainties were 170 K, 0.28 dex, 0.60 kG, 2.5 km s$^{-1}$ for $T_{rm eff}$, $log$ g, B, and $v sin i$, respectively. We determined B for 41 Taurus YSOs (upper limits for the remainder) and find systematic offsets (lower $T_{rm eff}$, higher $log$ g and $v sin i$) in parameters when B is measurable but not considered in the fit. The average $log$ g for the Class II and Class III objects differs by 0.23$pm$0.05dex, which is consistent with Class III objects being the more evolved members of the star-forming region. However, the dispersion in $log$ g is greater than the uncertainties, which highlights how the YSO classification correlates with age ($log$ g), yet there are exceptionally young (lower $log$ g) Class III YSOs and relatively old (higher $log$ g) Class II YSOs with unexplained evolutionary histories. The spectra from this work are provided in an online repository along with TW Hydrae Association (TWA) comparison objects and the model grid used in our analysis.
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