  We present the first sub-arcminute images of the Galactic Center above 10
keV, obtained with NuSTAR. NuSTAR resolves the hard X-ray source IGR
J17456-2901 into non-thermal X-ray filaments, molecular clouds, point sources
and a previously unknown central component of hard X-ray emission (CHXE).
NuSTAR detects four non-thermal X-ray filaments, extending the detection of
their power-law spectra with $\Gamma\sim1.3$-$2.3$ up to ~50 keV. A
morphological and spectral study of the filaments suggests that their origin
may be heterogeneous, where previous studies suggested a common origin in young
pulsar wind nebulae (PWNe). NuSTAR detects non-thermal X-ray continuum emission
spatially correlated with the 6.4 keV Fe K$\alpha$ fluorescence line emission
associated with two Sgr A molecular clouds: MC1 and the Bridge. Broad-band
X-ray spectral analysis with a Monte-Carlo based X-ray reflection model
self-consistently determined their intrinsic column density ($\sim10^{23}$
cm$^{-2}$), primary X-ray spectra (power-laws with $\Gamma\sim2$) and set a
lower limit of the X-ray luminosity of Sgr A* flare illuminating the Sgr A
clouds to $L_X \stackrel{>}{\sim} 10^{38}$ erg s$^{-1}$. Above ~20 keV, hard
X-ray emission in the central 10 pc region around Sgr A* consists of the
candidate PWN G359.95-0.04 and the CHXE, possibly resulting from an unresolved
population of massive CVs with white dwarf masses $M_{\rm WD} \sim 0.9
M_{\odot}$. Spectral energy distribution analysis suggests that G359.95-0.04 is
likely the hard X-ray counterpart of the ultra-high gamma-ray source HESS
J1745-290, strongly favoring a leptonic origin of the GC TeV emission.
