Neutron stars and Constraints for the Equation of State of Dense Matter

Neutron stars provide a natural laboratory for studying the properties of dense nuclear matter under extreme conditions. In this proceeding, we review our current understanding of dense isospin symmetric and asymmetric matter and neutron star physics. We focus on modern theoretical, experimental, and observational constraints, including first-principle calculations from lattice and perturbative Quantum Chromodynamics (QCD), as well as chiral effective field theory approaches at nuclear densities. From the experimental perspective, constraints on the equation of state arise from heavy-ion collisions, low-energy nuclear physics, and astrophysical observations, including neutron star masses, radii, and gravitational wave signatures from mergers. These multidisciplinary comparisons are crucial for bridging the gap between nuclear physics and astrophysical observations, in order to expand our knowledge of matter at supra-nuclear densities.