We report some results from one of the largest hydrodynamical cosmological simulations of large scale structures that has been done up to date. The MareNostrum Universe SPH simulation consists of 2 billion particles (2 times 1024^3) in a cubic box of 500 h^-1 Mpc on a side. This simulation has been done in the MareNostrum parallel supercomputer at the Barcelona SuperComputer Center. Due to the large simulated volume and good mass resolution, our simulated catalog of dark matter halos comprises more than half a million objects with masses larger than a typical Milky Way galaxy halo. From this dataset we have studied several statistical properties such as the evolution of the halo mass function, the void distribution, the shapes of dark and gas halos and the large scale distribution of baryons.