Dyson-Schwinger equations: Density, temperature and continuum strong QCD

Continuum strong QCD is the application of models and continuum quantum fie ld theory to the study of phenomena in hadronic physics, which includes; e. g., the spectrum of QCD bound states and their interactions; and the transi tion to, and properties of, a quark gluon plasma. We provide a contemporary perspective, couched primarily in terms of the Dyson-Schwinger equations b ut also making comparisons with other approaches and models. Our discourse provides a practitioners' guide to features of the Dyson-Schwinger equation s [such as confinement and dynamical chiral symmetry breaking] and canvasse s phenomenological applications to light meson and baryon properties in col d, sparse QCD. These provide the foundation for an extension to hot, dense QCD, which is probed via the introduction of the intensive thermodynamic va riables: chemical potential and temperature. We describe order parameters w hose evolution signals deconfinement and chiral symmetry restoration, and c hronicle their use in demarcating the quark gluon plasma phase boundary and characterising the plasma's properties. Hadron traits change in an equilib rated plasma. We exemplify this and discuss putative signals of the effects . Finally, since plasma formation is not an equilibrium process, we discuss recent developments in kinetic theory and its application to describing th e evolution from a relativistic heavy ion collision to an equilibrated quar k gluon plasma.