  In these notes we discuss recent developments in the field of non-equilibrium
quantum dynamics. Specifically, we consider nearly coherent Bose gases brought
far out of equilibrium and study their behaviour in view of connections between
universal properties, (quasi-)topological field configurations and turbulent
dynamics. We demonstrate that the isolated Bose gas, on its way back to thermal
equilibrium, can approach metastable non-equilibrium configurations and spend a
long time in their vicinity. In such configurations, which have been termed
non-thermal fixed points, the system shows universal long-range properties
manifest through scaling, i.e., self-similar correlations. The spatial field
pattern, at the same time, is characterized by the appearance of defects and
domain formation whose geometry gives rise to the particular scaling laws seen
in the correlation functions. We obtain an overall picture which connects
well-known concepts for describing universal dynamics such as wave-turbulence,
superfluid turbulence, and (quasi-)topological excitations. This allows to
bring together a wide range of concepts and methods with a large spectrum of
applications.
