  We present a new and complete library of synthetic spectra for modeling the
component of emission that is reflected from an illuminated accretion disk. The
spectra were computed using an updated version of our code XILLVER that
incorporates new routines and a richer atomic data base. We offer in the form
of a table model an extensive grid of reflection models that cover a wide range
of parameters. Each individual model is characterized by the photon index
\Gamma of the illuminating radiation, the ionization parameter \xi at the
surface of the disk (i.e., the ratio of the X-ray flux to the gas density), and
the iron abundance A_{Fe} relative to the solar value. The ranges of the
parameters covered are: 1.2 \leq \Gamma \leq 3.4, 1 \leq \xi \leq 10^4, and 0.5
\leq A_{Fe} \leq 10. These ranges capture the physical conditions typically
inferred from observations of active galactic nuclei, and also stellar-mass
black holes in the hard state. This library is intended for use when the
thermal disk flux is faint compared to the incident power-law flux. The models
are expected to provide an accurate description of the Fe K emission line,
which is the crucial spectral feature used to measure black hole spin. A total
of 720 reflection spectra are provided in a single FITS
file{\url{http://hea-www.cfa.harvard.edu/~javier/xillver/}} suitable for the
analysis of X-ray observations via the atable model in XSPEC. Detailed
comparisons with previous reflection models illustrate the improvements
incorporated in this version of XILLVER.
