Introduction.- Reduced Density Operators.- Correlations due to the Spin Statistics.- Mean-Field Approximation.- Correlations and their Dynamics.- Non-Markovian Effects.- Kinetic Equations with Selfenergy.- Properties of the Kinetic Equation.- T-Matrix Approximation.- Random Phase Approximation.- Screened Ladder Approximation.- Charged Carriers in EM Fields.- Non-Equilibrium Green's Functions.- Kinetics vs. Molecular Dynamics.- Conclusion.

This book presents quantum kinetic theory in a comprehensive way. The focus is on density operator methods and on non-equilibrium Green functions. The theory allows to rigorously treat nonequilibrium dynamics in quantum many-body systems. Of particular interest are ultrafast processes in plasmas, condensed matter and trapped atoms that are stimulated by rapidly developing experiments with short pulse lasers and free electron lasers. To describe these experiments theoretically, the most powerful approach is given by non-Markovian quantum kinetic equations that are discussed in detail, including computational aspects.