  We present the BACCO project, a simulation framework specially designed to
provide highly-accurate predictions for the distribution of mass, galaxies, and
gas as a function of cosmological parameters. In this paper, we describe our
main suite of simulations (L $\sim2$ Gpc and $4320^3$ particles) and present
various validation tests. Using a cosmology-rescaling technique, we predict the
nonlinear mass power spectrum over the redshift range $0<z<1.5$ and over scales
$10^{-2} < k/(h Mpc^{-1} ) < 5$ for 800 points in an 8-dimensional cosmological
parameter space. For an efficient interpolation of the results, we build an
emulator and compare its predictions against several widely-used methods. Over
the whole range of scales considered, we expect our predictions to be accurate
at the 2\% level for parameters in the minimal $\Lambda$ CDM model and to 3\%
when extended to dynamical dark energy and massive neutrinos. We make our
emulator publicly available under http://www.dipc.org/bacco
