The IUE Atlas of B-type Stellar Spectra is an atlas of B-type spectra consisting of short-wavelength, high-resolution data from the International Ultraviolet Explorer archive, designed to complement the widely used O-star atlas from the same source (Walborn, Nichols-Bohlin, & Panek 1985, NASA Reference Publication 1155, catalog <III/115>). The atlas presented here completes the OB natural group, i.e., to spectral type B3 for the main sequence and giants, type B5 at class Ib, and B8 at Ia, which is also the most relevant domain for stellar-wind effects among normal B-type spectra. Introduction: A primary objective of the IUE Atlas of B-type Stellar Spectra is to chart in detail the gradual disappearance of the stellar-wind features in normal spectra as a function of spectral type and luminosity class. As in the O-star atlas, which first demonstrated the strong correlation between the optical spectral types and the UV wind behaviour in the majority of the stars, the principal selection criterion was the existence of high-weight optical spectral classifications, which are quoted here without any revisions based upon the UV data. Some peculiar categories also are presented including a number of hypergiants, stars of types BN/BC (and including three of type O9.7 acquired since the O Atlas), and stars with enhanced winds. 86 images have been selected from the IUE archive for the atlas. The processing and presentation is as similar as possible to the O-star atlas, with the SWP data (roughly 1200-1900 angstrom range) rectified and rebinned to a uniform resolution of 0.25 angstrom. The conclusions from the B Star Atlas are similar to those from the O Star Atlas, namely, that the UV stellar-wind features display strong systematic trends as a functions of spectral type and luminosity class, and a high degree of correlation with the optical classifications as the winds decline toward the later types. A somewhat higher rate of exceptions to these correlations can be recognized among the B spectra (11%) than the O (2%), but they remain a small fractions of the total sample and do not prevent clear delineation of the normal behaviour. Indeed, it is only as a result of the latter that the exceptions can be identified and described.