The paper introduces a new high-resolution cosmological hydrodynamics code called RAMSES, which is designed to study structure formation in the universe with high spatial resolution. The code employs Adaptive Mesh Refinement (AMR) technology, using a tree-based data structure for recursive grid refinement. The N-body solver is similar to the one used in the ART code, while the hydrodynamical solver is based on a second-order Godunov method, known for its accuracy in capturing shock waves. The accuracy of the code is validated through various test cases, including pure gas dynamical tests and cosmological simulations. The specific refinement strategy in cosmological simulations is described, and potential spurious effects associated with shock wave propagation in the AMR grid are discussed, found to be negligible. The results from a large N-body and hydrodynamical simulation of structure formation in a low-density ΛCDM universe, with 256³ particles and 4.1 × 10⁷ cells in the AMR grid, reaching a formal resolution of 8192³, are presented. Convergence analysis of quantities such as dark matter density power spectrum, gas pressure power spectrum, and individual halo temperature profiles shows that numerical results are converging to the actual resolution limit of the code and are well reproduced by recent analytical predictions in the halo model framework.The paper introduces a new high-resolution cosmological hydrodynamics code called RAMSES, which is designed to study structure formation in the universe with high spatial resolution. The code employs Adaptive Mesh Refinement (AMR) technology, using a tree-based data structure for recursive grid refinement. The N-body solver is similar to the one used in the ART code, while the hydrodynamical solver is based on a second-order Godunov method, known for its accuracy in capturing shock waves. The accuracy of the code is validated through various test cases, including pure gas dynamical tests and cosmological simulations. The specific refinement strategy in cosmological simulations is described, and potential spurious effects associated with shock wave propagation in the AMR grid are discussed, found to be negligible. The results from a large N-body and hydrodynamical simulation of structure formation in a low-density ΛCDM universe, with 256³ particles and 4.1 × 10⁷ cells in the AMR grid, reaching a formal resolution of 8192³, are presented. Convergence analysis of quantities such as dark matter density power spectrum, gas pressure power spectrum, and individual halo temperature profiles shows that numerical results are converging to the actual resolution limit of the code and are well reproduced by recent analytical predictions in the halo model framework.