Individual chemical abundances for 14 elements (C, O, Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Mn, Fe, and Ni) are derived for a sample of M dwarfs using high-resolution, near-infrared H-band spectra from the Sloan Digital Sky Survey-IV/Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. The quantitative analysis included synthetic spectra computed with 1D LTE plane-parallel MARCS models using the APOGEE Data Release 17 line list to determine chemical abundances. The sample consists of 11 M dwarfs in binary systems with warmer FGK dwarf primaries and 10 measured interferometric angular diameters. To minimize atomic diffusion effects, [X/Fe] ratios are used to compare M dwarfs in binary systems and literature results for their warmer primary stars, indicating good agreement (<0.08 dex) for all studied elements. The mean abundance difference in primaries minus this work's M dwarfs is -0.05 ± 0.03 dex. It indicates that M dwarfs in binary systems are a reliable way to calibrate empirical relationships. A comparison with abundance, effective temperature, and surface gravity results from the APOGEE Stellar Parameter and Chemical Abundances Pipeline (ASPCAP) Data Release 16 finds a systematic offset of [M/H], T eff, log g = +0.21 dex, -50 K, and 0.30 dex, respectively, although ASPCAP [X/Fe] ratios are generally consistent with this study. The metallicities of the M dwarfs cover the range of [Fe/H] = -0.9 to +0.4 and are used to investigate Galactic chemical evolution via trends of [X/Fe] as a function of [Fe/H]. The behavior of the various elemental abundances [X/Fe] versus [Fe/H] agrees well with the corresponding trends derived from warmer FGK dwarfs, demonstrating that the APOGEE spectra can be used to examine Galactic chemical evolution using large samples of selected M dwarfs.