  Cosmological inference with large galaxy surveys requires theoretical models
that combine precise predictions for large-scale structure with robust and
flexible galaxy formation modelling throughout a sufficiently large cosmic
volume. Here, we introduce the MillenniumTNG (MTNG) project which combines the
hydrodynamical galaxy formation model of IllustrisTNG with the large volume of
the Millennium simulation. Our largest hydrodynamic simulation, covering (500
Mpc/h)^3 = (740 Mpc)^3, is complemented by a suite of dark-matter-only
simulations with up to 4320^3 dark matter particles (a mass resolution of 1.32
x 10^8 Msun/h) using the fixed-and-paired technique to reduce large-scale
cosmic variance. The hydro simulation adds 4320^3 gas cells, achieving a
baryonic mass resolution of 2 x 10^7 Msun/h. High time-resolution merger trees
and direct lightcone outputs facilitate the construction of a new generation of
semi-analytic galaxy formation models that can be calibrated against both the
hydro simulation and observation, and then applied to even larger volumes -
MTNG includes a flagship simulation with 1.1 trillion dark matter particles and
massive neutrinos in a volume of (3000 Mpc)^3. In this introductory analysis we
carry out convergence tests on basic measures of non-linear clustering such as
the matter power spectrum, the halo mass function and halo clustering, and we
compare simulation predictions to those from current cosmological emulators. We
also use our simulations to study matter and halo statistics, such as halo bias
and clustering at the baryonic acoustic oscillation scale. Finally we measure
the impact of baryonic physics on the matter and halo distributions.
