The paper presents a hydrodynamic simulation, "Illustris," that traces the evolution of galaxies from 12 million years after the Big Bang to the present epoch. The simulation covers a volume of (106.5 Mpc)$^3$ with 12 billion resolution elements, achieving a dark matter mass resolution of $6.26 \times 10^6$ M$_{\odot}$ and a baryonic mass resolution of $1.26 \times 10^6$ M$_{\odot}$. It successfully reproduces the observed distribution of galaxies in clusters, the statistics of hydrogen on large scales, and the metal and hydrogen content of galaxies on small scales. The simulation overcomes previous limitations by using a novel hydrodynamic algorithm, AREPO, and a comprehensive model for galaxy formation physics, including star formation, supermassive black hole feedback, and their effects on the environment. The results demonstrate that the ΛCDM model can accurately describe observational data on both large and small scales, and show a strong, scale-dependent impact of baryonic effects on the dark matter distribution. The simulation also provides insights into the formation of low-mass galaxies and the impact of baryons on the matter power spectrum, highlighting the need for high-resolution hydrodynamic simulations to achieve precision cosmology.The paper presents a hydrodynamic simulation, "Illustris," that traces the evolution of galaxies from 12 million years after the Big Bang to the present epoch. The simulation covers a volume of (106.5 Mpc)$^3$ with 12 billion resolution elements, achieving a dark matter mass resolution of $6.26 \times 10^6$ M$_{\odot}$ and a baryonic mass resolution of $1.26 \times 10^6$ M$_{\odot}$. It successfully reproduces the observed distribution of galaxies in clusters, the statistics of hydrogen on large scales, and the metal and hydrogen content of galaxies on small scales. The simulation overcomes previous limitations by using a novel hydrodynamic algorithm, AREPO, and a comprehensive model for galaxy formation physics, including star formation, supermassive black hole feedback, and their effects on the environment. The results demonstrate that the ΛCDM model can accurately describe observational data on both large and small scales, and show a strong, scale-dependent impact of baryonic effects on the dark matter distribution. The simulation also provides insights into the formation of low-mass galaxies and the impact of baryons on the matter power spectrum, highlighting the need for high-resolution hydrodynamic simulations to achieve precision cosmology.