This chapter on the physics of compact objects begins with a section on white dwarfs. It will be shown that the famous Chandrasekhar equation is just the relativistic Thomas–Fermi equation. For white dwarfs the Thomas–Fermi approximation is ideally justified. For neutron stars the general relativistic stellar structure equations are needed. In view of the fact that we do not have an accurate quantitative understanding of neutron stars, we begin with a brief qualitative overview of the interior of neutron stars and discuss some simplified models. Then we turn to the equation of state at high densities. Since the densities in the central regions of neutron stars can be almost an order of magnitude higher than the nuclear density, we need a reliable equation of state at super-nuclear densities. This is a very difficult problem and large uncertainties remain. In spite of this, it is possible to establish reliable, rather tight upper limits of the largest possible mass of a non-rotating neutron star. This plays a decisive role in the observational identification of black holes, to be discussed in Chap. 7. Additional sections are devoted to rotating neutron stars, the cooling of neutron stars, and to neutron stars in binaries.