  We report the results of our study of the energy spectra and absolute fluxes
of cosmic rays (CRs) in the Local Galaxy based on a five-year $\gamma$-ray
observation with the Fermi Large Area Telescope (LAT) of eight nearby giant
molecular clouds (GMCs) belonging to the Gould Belt. The $\gamma$-ray signals
obtained with high statistical significance allow the determination of
$\gamma$-ray spectra above 300~MeV with adequate precision for extraction of
the energy distributions of CRs in these clouds. Remarkably, both the derived
spectral indices and the absolute fluxes of CR protons in the energy interval
$10 - 100~ \rm \ GeV$ agree with the recent direct measurements of local CRs by
the PAMELA experiment. This is strong evidence of a quite homogeneous
distribution of CRs, at least within several hundred parsecs of the Local
Galaxy. Combined with the well established energy-dependent time of escape of
CRs from the Galaxy, $\tau(E) \propto E^{-\delta}$ with $\delta \approx
0.5-0.6$, the measured spectrum implies a CR spectral index of the
(acceleration) source of $\approx$E$^{-2.3}$. At low energies, the spectra of
$\gamma$ rays appear to vary from one cloud to another. This implies spatial
variations of the energy spectra of CRs below 10~GeV, which at such low
energies could be explained naturally by both the impact of the propagation
effects and the contribution of CR locally accelerated inside the clouds.
