  We introduce the new TNG-Cluster project, an addition to the IllustrisTNG
suite of cosmological magnetohydrodynamical simulations of galaxy formation.
Our objective is to significantly increase the statistical sampling of the most
massive and rare objects in the Universe: galaxy clusters with log(M_200c /
Msun) > 14.3 - 15.4 at z=0. To do so, we re-simulate 352 cluster regions drawn
from a 1 Gpc volume, thirty-six times larger than TNG300, keeping entirely
fixed the IllustrisTNG physical model as well as the numerical resolution. This
new sample of hundreds of massive galaxy clusters enables studies of the
assembly of high-mass ellipticals and their supermassive black holes (SMBHs),
brightest cluster galaxies (BCGs), satellite galaxy evolution and environmental
processes, jellyfish galaxies, intracluster medium (ICM) properties, cooling
and active galactic nuclei (AGN) feedback, mergers and relaxedness, magnetic
field amplification, chemical enrichment, and the galaxy-halo connection at the
high-mass end, with observables from the optical to radio synchrotron and the
Sunyaev-Zeldovich (SZ) effect, to X-ray emission, as well as their cosmological
applications. We present an overview of the simulation, the cluster sample,
selected comparisons to data, and a first look at the diversity and physical
properties of our simulated clusters and their hot ICM.
