We introduce the Uchuu suite of large high-resolution cosmological N -body simulations . The largest simulation , named Uchuu , consists of 2.1 trillion ( 12800 ^ { 3 } ) dark matter particles in a box of 2.0 h ^ { -1 } Gpc , and the mass of each particle is 3.27 \times 10 ^ { 8 } h ^ { -1 } M _ { \odot } . The highest resolution simulation , called Shin-Uchuu , consists of 262 billion ( 6400 ^ { 3 } ) particles in a box of 140 h ^ { -1 } Mpc , with a particle mass of 8.97 \times 10 ^ { 5 } h ^ { -1 } M _ { \odot } . Combining these simulations we can follow the evolution of dark matter haloes ( and subhaloes ) spanning from dwarf galaxies to massive galaxy cluster hosts . We present basic statistics , dark matter power spectra and halo ( subhalo ) mass function , to demonstrate the huge dynamic range and superb statistics of the Uchuu simulations . From the analysis of the evolution of the power spectra we conclude that our simulations are accurate enough from the Baryon Acoustic Oscillations up to very small scales . We also provide parameters of a mass-concentration model , which describes the evolution of halo concentrations , that reproduces our simulation data within 5 % error . We make publicly available various N -body products , as part of Uchuu Data Release 1 , on the Skies & Universes site . We also plan to release gravitational lensing maps , mock galaxy , X-ray cluster and active galactic nuclei catalogues in the near future .