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\title{\bf Far--from--Equilibrium Quantum Fields\\and Thermalization}
\author{J\"urgen Berges\thanks{email: J.Berges@thphys.uni--heidelberg.de} \ and Markus M. M\"uller\thanks{email: M.M.Mueller@thphys.uni--heidelberg.de}\\Universit\"at Heidelberg, Institut f\"ur Theoretische Physik\\Philosophenweg 16, 69120 Heidelberg, Germany}
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\begin{abstract}
We compute the nonequilibrium real-time
evolution of an $O(N)$--sym\-metric scalar quantum field theory from a 
systematic $2PI$--$1/N$ expansion to next-to-leading order, which includes 
scattering and memory effects. The corresponding ``full'' Kadanoff-Baym 
equation is solved numerically without further approximations. This allows us 
to obtain a controlled description of far-from-equilibrium dynamics, and the 
late-time approach to quantum thermal equilibrium. We compare the numerical 
solution to an approximate kinetic description based on a gradient expansion.
\end{abstract}

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