From January 1998 to July 1999, Lunar Prospector continuously measured the leakage flux of neutrons from the Moon in four distinct energy ranges from 0 eV to 8 MeV. These measurements were made using two 3He tubes within the Neutron Spectrometer (NS) and the anticoincidence shield of the Gamma-Ray Spectrometer (GRS). This publication details the reduction of raw neutron data (level 0) to develop four maps of neutron counting rates, which can be interpreted in terms of elemental composition of the lunar regolith. Details are given to convert level 0 data into level 1 data, where corrupted and unusable records have been removed because of transmission errors, solar energetic-particle events, or cross-talk with other instruments. At level 2, time series data have been corrected for observational biases and variations of the response function of the instruments. At level 3 the highest-quality neutron data (low-altitude, high time resolution) are mapped onto the Moon. The main characteristics of each map are, for thermal neutrons, energy range 0--0.4 eV, dynamic range 95%, precision 2.7%, and half width at half maximum (HWHM) resolution 23 km, in units of counts/8-s; for epithermal neutrons, energy range 0.4 eV < E < 0.7 MeV, dynamic range 15%, precision 1%, and HWHM resolution 22 km, in units of counts/8-s; for moderated neutrons, energy range 0--0.8 MeV, dynamic range 15%, precision 1.8%, and HWHM resolution <45 km, in units of counts/32-s; and for fast neutrons, energy range 0.8--8 MeV, dynamic range 30%, precision 1.6%, and HWHM resolution 23 km, in units of counts/32-s. All maps are normalized to 30 km altitude, at the equator; and to the flux of cosmic rays in January 1998. They are presented as 720 ¿ 360 arrays equally spaced in latitude and longitude. Results are reproducible from raw data that are available at the Planetary Data System (PDS), together with guidance and numerical values in this publication.