  In this work we study the non-equilibrium dynamics of a quark-gluon plasma,
as created in heavy-ion collisions. We investigate how big of a role plasma
instabilities can play in the isotropization and equilibration of a quark-gluon
plasma. In particular, we determine, among other things, how much collisions
between the particles can reduce the growth rate of unstable modes. This is
done both in a model calculation using the hard-loop approximation, as well as
in a real-time lattice simulation combining both classical Yang-Mills-fields as
well as inter-particle collisions. The new extended version of the simulation
is also used to investigate jet transport in isotropic media, leading to a
cutoff-independent result for the transport coefficient q-hat. The precise
determination of such transport coefficients is essential, since they can
provide important information about the medium created in heavy-ion collisions.
In anisotropic media, the effect of instabilities on jet transport is studied,
leading to a possible explanation for the experimental observation that
high-energy jets traversing the plasma perpendicular to the beam axis
experience much stronger broadening in rapidity than in azimuth. The
investigation of collective modes in the hard-loop limit is extended to
fermionic modes, which are shown to be all stable. Finally, we study the
possibility of using high energy photon production as a tool to experimentally
determine the anisotropy of the created system. Knowledge of the degree of
local momentum-space anisotropy reached in a heavy-ion collision is essential
for the study of instabilities and their role for isotropization and
thermalization, because their growth rate depends strongly on the anisotropy
