This volume presents an authoritative review of the physics of strongly and electroweakly interacting elementary particle matter in extreme conditions that prevailed in the very early Universe, and which are being recreated in high energy physics laboratories today. Exciting, high-quality experimental results from RHIC collider at Brookhaven, collected since summer 2000, suggest that strongly interacting quark-gluon plasma has indeed been produced. The study of these phenomena will form an important part of theoretical particle and nuclear physics for years to come. Based on the discussions of more than a hundred experts at the Strong and Electroweak Matter 2004 Meeting, this volume contains an up-to-date overview of present ideas on QCD matter quark-gluon plasma in heavy ion collisions, phase structure, kinetics, thermalization and transport properties. Also discussed are topics related to the cosmology of the early Universe, dark matter, inflation and creation of particle-antiparticle asymmetries. Both analytic and numerical lattice Monte Carlo methods are emphasized.