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The aim of this thesis is to use a cross-match between WISE, 2MASS and SDSS to identify a large sample of M dwarfs. Through the careful characterisation and quality control of these M dwarfs I aim to identify rare systems (i.e. unresolved UCD companions, young M dwarfs, late M dwarfs and M dwarfs with common proper motion companions). Locating ultracool companions to M dwarfs is important for constraining low-mass formation models, the measurement of substellar dynamical masses and radii, and for testing ultracool evolutionary models. This is done by using an optimised method for identifying M dwarfs which may have unresolved ultracool companions. To do this I construct a catalogue of 440 694 M dwarf candidates, from WISE, 2MASS and SDSS, based on optical- and near-infrared colours and reduced proper motion. With strict reddening, photometric and quality constraints I isolate a sub-sample of 36 898 M dwarfs and search for possible mid-infrared M dwarf + ultracool dwarf candidates by comparing M dwarfs which have similar optical/near-infrared colours (chosen for their sensitivity to effective temperature and metallicity). I present 1 082 M dwarf + ultracool dwarf candidates for follow-up. Using simulated ultracool dwarf companions to M dwarfs, I estimate that the occurrence of unresolved ultracool companions amongst my M dwarf + ultracool dwarf candidates should be at least four times the average for my full M dwarf catalogue. I discuss yields of candidates based on my simulations. The possible contamination and bias from misidentified M dwarfs is then discussed, from chance alignments with other M dwarfs and UCDs, from chance alignments with giant stars, from chance alignments with galaxies, and from blended systems (via visual inspection). I then use optical spectra from LAMOST to spectral type a subset of my M dwarf + ultracool dwarf candidates. These candidates need confirming as true M dwarf + ultracool dwarf systems thus I present a new method I developed to use low resolution near-infrared spectra which relies on two colour similar objects (one an excess candidate, one not) having very similar spectra. A spectral difference of these two colour similar objects should leave the signature of a UCD in the residual of their differences, which I look for using the difference in two spectral bands designed to identify UCD spectral features. I then present the methods used to identify other rare systems from my full M dwarf catalogue. Young M dwarfs were identified by measuring equivalent widths of Hα from the LAMOST spectra, and by measuring rotation periods from Kepler 2 light curves. I identify late M dwarfs photometrically (using reduced proper motion and colour cuts) and spectroscopically (using the LAMOST spectra with spectral indices from the literature). Also I present common proper motion analysis aimed at finding Tycho-2 primaries for my M dwarfs and look for physically separated M dwarf + M dwarf pairs (internally within my full M dwarf catalogue)

M Dwarfs from the SDSS, 2MASS and WISE Surveys: Identification, Characterisation and Unresolved Ultracool Companionship