Recent experiments carried out at the Relativistic Heavy Ion Collider at the Brookhaven National Laboratory provide strong evidence that a matter can be driven from a confined, low-temperature phase, observed in our every day world into a deconfined high-temperature phase of liberated quarks and gluons. The equilibrium and dynamical properties of the deconfining phase transition are thus of great theoretical interest, since they also provide an information about the first femtoseconds of the evolution of our Universe, when the hot primordial soup while cooling has undergone a chain of phase transitions. The aspects of the deconfining phase transition studied in this work include: the dynamics of the SU(3) gauge theory after the heating quench (which
models rapid heating in the heavy-ion collisions), equilibrium properties of the phase transition in the SU(3) gauge theory with boundaries at low temperature (small volumes at RHIC suggest that
boundary effects cannot be neglected and periodic boundary conditions normally used in lattice simulations do not correspond to the experimental situation), and a study of the order of the transition in U(1) gauge theory.
