We present high-resolution, high signal-to-noise ratio spectra of the QSO Q2206-199 obtained with HIRES on the 10 m W. M. Keck Telescope. Our analysis focuses on the two previously identified damped Ly alpha systems found at z = 1.920 and z = 2.076. For the z = 1.920 system, we measure accurate abundances (relative to solar) for Fe, Cr Si, Ni, Ti, and Zn: [Fe/H] = -0.705 +/- 0.097, [Cr/H] = -0.580 +/- 0.100, [Si/H] = -0.402 +/- 0.098, [Ni/H] = -1.012 +/- 0.095, [Ti/H] = -0.776 +/- 0.081, and [Zn/H] = -0.379 +/- 0.097. This system exhibits the highest metallicity we have measured for a damped Ly alpha system. By contrast the z = 2.076 system is the most metal poor ([Zn/H] < -1.745) we have analyzed, showing absorption features for only the strongest transitions. We determine accurate abundances for Fe, Si, and Al: [Fe/H] = -2.621 +/- 0.071, [Si/H] = -2.225 +/- 0.075, and [Al/H] = -2.727 +/- 0.070. Analyses of the abundance variations of Fe, Ni, Cr, and Si relative to Zn and the abundance trends versus condensation temperature do not offer positive evidence for the presence of dust in the damped system at z = 1.920. In addition, the relative abundance ratio [Ti/Fe] approximate to 0 further suggests the absence of ISM-like dust. Unfortunately, the lack of measurable Zn absorption in the z = 2.076 system does not allow a similar investigation for the presence of dust. In addition to the significant difference in the metallicity, the two damped systems have vastly different kinematic characteristics. The z = 1.920 system spans approximate to 150 km s(-1) in velocity space (measured from the low-ion transitions), while the z = 2.076 system spans a mere 30 km s(-1). Furthermore, the z = 1.920 profiles are significantly asymmetric, while the z = 2.076 profiles are highly symmetric. Even with these differences, we contend the two systems are consistent kinematically with one physical description, that of a thick, rotating disk. In addition to the two previously identified damped Ly alpha systems, we investigate a very strong Mg II system at z = 0.752, which we believe is a third damped Ly alpha system along the line of sight. The very weak Mn II lambda lambda 2606, 2594, 2576 and Ti II lambda lambda 3073, 3342, and 3384 transitions have been positively measured and suggest a very conservative lower limit H I abundance of log N(H I) > 19.0 assuming metallicity relative to solar equal to 0 and no depletion. Together with the damped system at z = 1.920, this marks the first confident (> 5 sigma) detection of Ti in QSO absorption-line systems. We analyze the abundance ratios ratios [Mn/Fe] and [Ti/Fe] and their values are inconsistent with significant dust depletion, yet consistent with the abundance pattern detected for halo stars in the Galaxy (Lu, Sargent, & Barlow 1996). 1996). Finally, we identify a C IV system at z = 2.014 that shows a very narrow feature in Si IV and C IV absorption. The corresponding b-values (5.5 and 8.9 km s(-1) for for Si IV and C IV, respectively) for this component suggest a temperature of 4.7 x 10(4) K. Because collisional ionization can explain the observed abundances only for T > 9 x 10(4) K, we contend these ions must have formed through a different physical process (e.g., photoionization).