  Atmospheric escape is a fundamental process that affects the structure,
composition, and evolution of many planets. The signatures of escape are
detectable on close-in, gaseous exoplanets orbiting bright stars, owing to the
high levels of extreme-ultraviolet irradiation from their parent stars. The
Colorado Ultraviolet Transit Experiment (CUTE) is a CubeSat mission designed to
take advantage of the near-ultraviolet stellar brightness distribution to
conduct a survey of the extended atmospheres of nearby close-in planets. The
CUTE payload is a magnifying NUV (2479~--~3306 Ang) spectrograph fed by a
rectangular Cassegrain telescope (206mm x 84mm); the spectrogram is recorded on
a back-illuminated, UV-enhanced CCD. The science payload is integrated into a
6U Blue Canyon Technology XB1 bus. CUTE was launched into a polar, low-Earth
orbit on 27 September 2021 and has been conducting this transit spectroscopy
survey following an on-orbit commissioning period. This paper presents the
mission motivation, development path, and demonstrates the potential for small
satellites to conduct this type of science by presenting initial on-orbit
science observations. The primary science mission is being conducted in
2022~--~2023, with a publicly available data archive coming on line in 2023.
