Strongly interacting (QCD) matter is expected to exhibit a multifaceted phase structure: a hadron gas at low temperatures, a quark-gluon plasma at very high temperatures, nuclear matter in the low-temperature and high-density region, color superconductors at high densities. Most of the conjectured phases cannot yet be scrutinized by experiments but are based on model calculations. This monograph investigates the phases of QCD using a nonlocal covariant extension of the Nambu und Jona-Lasinio (NJL) model. This allows one to take into account the running of the QCD coupling strength at high and...