  Hydrodynamical cosmological simulations are increasing their level of realism
by considering more physical processes and having greater resolution or larger
statistics. However, usually either the statistical power of such simulations
or the resolution reached within galaxies are sacrificed. Here, we introduce
the NewHorizon project in which we simulate at high resolution a zoom-in region
of $\sim(16\,\rm Mpc)^3$ that is larger than a standard zoom-in region around a
single halo and is embedded in a larger box. A resolution of up to 34 pc is
reached within galaxies; this allows the simulation to capture the multi-phase
nature of the interstellar medium and the clumpy nature of the star formation
process in galaxies. In this introductory paper, we present several key
fundamental properties of galaxies and their black holes, including the galaxy
mass function, cosmic star formation rate, galactic metallicities, the
Kennicutt-Schmidt relation, the stellar-to-halo mass relation, galaxy sizes,
stellar kinematics and morphology, gas content within galaxies and its
kinematics, and the black hole mass and spin properties over time. The various
scaling relations are broadly reproduced by NewHorizon with some differences
with the standard observables. Owing to its exquisite spatial resolution,
NewHorizon captures the inefficient process of star formation in galaxies,
which evolve over time from being more turbulent, gas rich, and star bursting
at high redshift. These high-redshift galaxies are also more compact, and they
are more elliptical and clumpier until the level of internal gas turbulence
decays enough to allow for the formation of discs. The NewHorizon simulation
gives access to a broad range of galaxy formation and evolution physics at
low-to-intermediate stellar masses, which is a regime that will become
accessible in the near future through surveys such as the LSST.
