  We present a systematic spectral analysis of 350 bright Gamma-Ray Bursts
(GRBs) observed with the Burst and Transient Source Experiment (BATSE; $\sim$
30 keV -- 2 MeV) with high temporal and spectral resolution. Our sample was
selected from the complete set of 2704 BATSE GRBs based on their energy fluence
or peak photon flux values to assure good statistics, and included 17 short
GRBs. To obtain well-constrained spectral parameters, several photon models
were used to fit each spectrum. We compared spectral parameters resulting from
the fits using different models, and the spectral parameters that best
represent each spectrum were statistically determined, taking into account the
parameterization differences among the models. A thorough analysis was
performed on 350 time-integrated and 8459 time-resolved burst spectra, and the
effects of integration times in determining the spectral parameters were
explored. Using the results, we studied correlations among spectral parameters
and their evolution pattern within each burst. The resulting spectral catalog
is the most comprehensive study of spectral properties of GRB prompt emission
to date, and is available electronically from the High-Energy Astrophysics
Science Archive Research Center (HEASARC). The catalog provides reliable
constraints on particle acceleration and emission mechanisms in GRBs.
