We report the results of a survey of the Galactic Center region (\mid l\mid < 2 DEG, \mid b\mid < 0.5 DEG) performed with the BeppoSAX satellite. The flux from the center of our Galaxy corresponds to a luminosity of ~3 1035 erg s-1 in the 2-10 keV range. Due to the limited angular resolution (\gsim1') only part of it is supposed to come from Sagittarius A*, the non-thermal radio source which is believed to mark the dynamical center of the Galaxy. In addition to the diffuse emission, several bright (LX\gsim1036 ergs s-1) point sources have been observed, both persistent (A 1742-294, SLX 1744-299, SLX 1744-300, 1E 1743.1-2843, 1E 1740.7-2942) and transient (XTE J1748-288, SAX J1747.0-2853 and KS 1741-293). The Low Mass X-ray Binary AX J1745.6-2901, discovered with ASCA at only 1.3' from SgrA* was detected in a low luminosity state in August 1997. The 1-150 keV spectrum of the hard X-ray source 1E 1740.7-2942 is well described by a Comptonization model, typical of black hole candidates in their low/hard state, with no evidence for strong Fe lines. The detection of a type I burst shows that the transient source SAX J1747.0-2853 (probably the same as the 1976 transient GX 0.2-0.2) is a LMXRB containing a neutron star. The transient black hole candidate XTE J1748-288 was detected at a luminosity (~ 1036 ergs s-1) consistent with the extrapolation of the exponential decay of the outburst observed with the XTE All Sky Monitor. Two fainter sources are very likely associated with young neutron stars: the (possibly diffuse) X-ray source at the center of the composite supernova remnant G0.9+0.1, and the ``head" of the axially symmetric radio source G359.23-0.92. The latter has been detected above ~ 6 keV, supporting a non-thermal emission mechanism.