The theory of quantum chromodynamics (QCD) is introduced. Features of QCD as the nontrivial vacuum due to quark and gluon condensate and asymptotic freedom at high-energy scales are discussed. The concept of perturbative QCD and the running of the coupling constant is established. The equation of state of QCD at high temperatures from lattice QCD is reviewed and confronted with perturbative QCD calculations. The QCD equation of state at high baryon density is discussed. Properties of selfbound stars are developed where the equation of state has a nonvanishing pressure at a nonvanishing energy density. The mass–radius relation of pure quark stars is examined and compared to the limits from causality.

As one of the core chapters, the general properties of compact stars are discussed. Spheres of fluid in hydrostatic equilibrium are studied within general relativity. The concept of the mass–radius relation is introduced for the classic case of a gas of noninteracting neutrons. Landau‘s argument for a maximum mass of neutron stars and white dwarfs is delineated. Thereby, the Landau mass and radius is defined for studying scaling solutions of the Tolman–Oppenheimer–Volkoff equation. The power of scaling arguments is demonstrated for the case of a free Fermi gas with arbitrary particle mass, a relativistic gas of fermions with a vacuum term, and the limiting equation of state from causality. The concept of selfbound stars is put forward, giving rise to limits on the compactness and the maximum density achievable for compact stars in general. Generic interactions between fermions are studied and their implications for compact star properties are derived. The general properties of compact stars made of bosons with and without interactions are also investigated.