The rich history of neutron stars, observationally as well as theoretically, is sketched. The different layers of a neutron star are discussed step-by-step. The outer crust is described as a lattice of nuclei with a sea of electrons. The nuclear shell model and the phenomenon of magic numbers are introduced. The sequence of nuclei in the outer crust of a neutron star is shown explicitly. Features of the inner crust, as nuclear superfluidity and superconductivity, and the connection to pulsar glitches and cooling of neutron stars are described. The possible appearance of geometric structures in the inner crust, the pasta phases, are discussed. The concept of nuclear matter is established. The present-day knowledge of the neutron matter equation of state is put in place. The mass–radius of neutron stars are conceptionally investigated with a detailed discussion of the stability of neutron star configurations. The possible presence of exotic matter in the inner core of neutron stars is considered. The experimental data on hypernuclei is summarized and the paradigm of the so-called hyperon puzzle for neutron stars is analyzed.