  We consider Bose gases consisting of $N$ particles trapped in a box with
volume one and interacting through a repulsive potential with scattering length
of the order $N^{-1}$(Gross-Pitaevskii regime). We determine the ground state
energy and the low-energy excitation spectrum, up to errors vanishing as $N \to
\infty$. Our results confirm Bogoliubov's predictions.
