We present a catalogue of H-band spectra for 85 stars of approximately solar abundance observed at a resolving power of 3000 with the KPNO Mayall 4m Fourier Transform Spectrometer. The atlas covers spectral types O7-M5 and luminosity classes I-V as defined on the MK system. The final reduced spectra are available in addition to data products used in the analysis of the paper such as Tables of equivalent width measurements for spectral features of interest in deriving effective temperatures and estimating luminosity classes of stars. The final spectra cover wavelength range 1.52 to 1.79 microns.