Due to their ubiquity and very long main-sequence lifetimes, M dwarfs provide an excellent tool to study the formation and chemical enrichment history of our Galaxy. However, owing to their intrinsic faintness, the acquisition of high-resolution, high signal-to-noise spectra of low-mass stars has been limited to small numbers of very nearby stars, mostly from the Galactic disk population. On the other hand, large numbers of low-resolution spectra of M-type dwarf stars from both the local Galactic disk and halo can be available from various surveys. In order to fully exploit these data, we develop a template-fit method using a set of empirically assembled M dwarf/subdwarf classification templates, based on the measurements of the TiO and CaH molecular bands near 7000 Å, which are used to classify M dwarfs/subdwarfs by spectral type and metallicity class. We further present a pipeline to automatically determine the effective temperature Teff, metallicity [M/H], alpha-element to iron abundance ratio [alpha/Fe], and surface gravity log(g) of M dwarfs/subdwarfs using the latest version of BT-Settl model atmospheres. We apply this pipeline to analyze the low-resolution (R∼2000) spectra of a set of 1700 high proper-motion stars in Chapter 2 and its improved version to a set of 3745 low/high proper-motion M dwarfs/subdwarfs in Chapter 3. These spectra were collected at the MDM Observatory, Lick Observatory, Kitt Peak National Observatory, and Cerro Tololo Interamerican Observatory. We examine variations of the inferred chemical parameters [M/H] and [alpha/Fe] in the HR diagram constructed from their Gaia DR2/EDR3 parallaxes and magnitudes. We also study the distribution of our stars in the abundance diagram of [alpha/Fe] versus [M/H] and inspect the variations of the parameters such as metallicity class MC, effective temperature Teff and surface gravity in this diagram. In addition, the variation of the derived chemical parameters in the kinematic planes is analyzed. The precision of the pipeline is confirmed by comparing the chemical parameters of the primaries and their companions in a set of binary systems