We present LITTLE THINGS (Local Irregulars That Trace Luminosity Extremes, The HI 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 HI-line data obtained with the National Radio Astronomy Observatory (NRAO) Very Large Array (VLA). The HI-line data are characterized by high sensitivity ({<=}1.1mJy/beam per channel), high spectral resolution ({<=}2.6km/s), and high angular resolution (~6"). The LITTLE THINGS sample contains dwarf galaxies that are relatively nearby ({<=}10.3Mpc; 6" is {<=}300pc), 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 HI map characteristics, and show channel maps, moment maps, velocity-flux profiles, and surface gas density profiles. In addition to the HI data we have GALEX UV and ground-based UBV and H{alpha} 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.