  We present results of an all-sky hard X-ray survey based on almost four years
of observations with the IBIS telescope on board the INTEGRAL observatory. The
dead time-corrected exposure of the survey is ~33 Ms. Approximately 12% and 80%
of the sky have been covered to limiting fluxes lower than 1 and 5 mCrab,
respectively. Our catalog of detected sources includes 400 objects, 339 of
which exceed a 5 sigma detection threshold on the time-averaged map of the sky
and the rest were detected in various subsamples of exposures. Among the
identified sources, 213 are Galactic (87 low-mass X-ray binaries, 74 high-mass
X-ray binaries, 21 cataclysmic variables, 6 coronally active stars, and other
types) and 136 are extragalactic, including 131 active galactic nuclei (AGNs)
and 3 clusters of galaxies. We obtained number-flux functions for AGNs and
Galactic sources. The logN-logS relation of AGNs (excluding blazars) is based
on 69 sources with fluxes higher than S_lim=1.1 x 10^{-11} erg/s/cm^2 (~0.8
mCrab) in the 17-60 keV energy band. The cumulative number-flux function of
AGNs located at Galactic latitudes $|b|>5^\circ$, where the survey is
characterized by high identification completeness, can be described by a power
law with a slope of 1.62 +/- 0.15 and normalization of (5.7 +/- 0.7) x 10^{-3}
sources per deg^2 at fluxes >1.43 x 10^{-11} erg/s/cm^2 (>1 mCrab). AGNs with
fluxes higher than S_lim make up ~1% of the cosmic X-ray background at 17-60
keV. We present evidence of strong inhomogeneity in the spatial distribution of
nearby (<70 Mpc) AGNs, which reflects the large-scale structure in the local
Universe.
