We present LITTLE THINGS (Local Irregulars That Trace Luminosity Extremes, The H I Nearby Galaxy Survey), which is aimed at determining what drives star formation in dwarf galaxies. This is a multi-wavelength survey of 37 dwarf irregular and 4 blue compact dwarf galaxies that is centered around H I -line data obtained with the National Radio Astronomy Observatory (NRAO) Very Large Array (VLA). The H I -line data are characterized by high sensitivity (≤1.1 mJy beam –1 per channel), high spectral resolution (≤2.6 km s –1 ), and high angular resolution (~6”). The LITTLE THINGS sample contains dwarf galaxies that are relatively nearby (≤10.3 Mpc; 6” is ≤300 pc), that were known to contain atomic hydrogen, the fuel for star formation, and that cover a large range in dwarf galactic properties. We describe our VLA data acquisition, calibration, and mapping procedures, as well as H I map characteristics, and show channel maps, moment maps, velocity-flux profiles, and surface gas density profiles. In addition to the H I data we have GALEX UV and ground-based UBV and Hα images for most of the galaxies, and JHK images for some. Spitzer mid-IR images are available for many of the galaxies as well. These data sets are available online.