The EAGLE project is a suite of hydrodynamical simulations that model the formation of galaxies and supermassive black holes in a standard ΛCDM universe. The simulations aim to reproduce the observed galaxy stellar mass function (GSMF) and other galaxy properties by calibrating feedback mechanisms from star formation and active galactic nuclei (AGN). The simulations use high-resolution numerical techniques and subgrid models to account for unresolved physical processes, such as radiative cooling, star formation, and feedback from massive stars and AGN. The feedback is implemented in a way that allows galactic winds to develop without predetermined speed or mass loading factors, and the efficiency of feedback is calibrated to match the observed GSMF and the relation between stellar mass and black hole mass. The simulations also include variations in numerical techniques and higher-resolution zoomed-in volumes to test the robustness of the predictions. The results show good agreement with a range of observables, including specific star formation rates, passive fractions, the Tully-Fisher relation, and column density distributions of intergalactic metals. However, the mass-metallicity relations for gas and stars are insufficiently steep at lower masses. The simulations also include a detailed description of the subgrid physics, including radiative cooling, reionisation, star formation, stellar mass loss and metal enrichment, energy feedback from star formation, and AGN feedback. The simulations are calibrated to match the observed GSMF and other galaxy properties, and they provide a valuable resource for studying galaxy formation. The results show that the simulations can make robust, quantitative predictions for more diffuse components, such as the low-density intergalactic medium and the outer parts of galaxy clusters. The simulations also provide insights into the physical processes that govern galaxy formation and evolution, including the role of feedback in regulating star formation and the interplay between gas and dark matter. The simulations are part of a larger effort to understand the formation and evolution of galaxies and their environments in the context of cosmological theory.The EAGLE project is a suite of hydrodynamical simulations that model the formation of galaxies and supermassive black holes in a standard ΛCDM universe. The simulations aim to reproduce the observed galaxy stellar mass function (GSMF) and other galaxy properties by calibrating feedback mechanisms from star formation and active galactic nuclei (AGN). The simulations use high-resolution numerical techniques and subgrid models to account for unresolved physical processes, such as radiative cooling, star formation, and feedback from massive stars and AGN. The feedback is implemented in a way that allows galactic winds to develop without predetermined speed or mass loading factors, and the efficiency of feedback is calibrated to match the observed GSMF and the relation between stellar mass and black hole mass. The simulations also include variations in numerical techniques and higher-resolution zoomed-in volumes to test the robustness of the predictions. The results show good agreement with a range of observables, including specific star formation rates, passive fractions, the Tully-Fisher relation, and column density distributions of intergalactic metals. However, the mass-metallicity relations for gas and stars are insufficiently steep at lower masses. The simulations also include a detailed description of the subgrid physics, including radiative cooling, reionisation, star formation, stellar mass loss and metal enrichment, energy feedback from star formation, and AGN feedback. The simulations are calibrated to match the observed GSMF and other galaxy properties, and they provide a valuable resource for studying galaxy formation. The results show that the simulations can make robust, quantitative predictions for more diffuse components, such as the low-density intergalactic medium and the outer parts of galaxy clusters. The simulations also provide insights into the physical processes that govern galaxy formation and evolution, including the role of feedback in regulating star formation and the interplay between gas and dark matter. The simulations are part of a larger effort to understand the formation and evolution of galaxies and their environments in the context of cosmological theory.