Nanoscale miniaturization and femtosecond laser-pulse spectroscopy require a quantum mechanical description of the carrier kinetics that goes beyond the conventional Boltzmann theory. On these extremely short length and time scales, the electrons behave as do partially coherent waves. This monograph deals with quantum kinetics for transport in low-dimensional microstructures and for ultra-short laser pulse spectroscopy. The nonequilibrium Green function theory is described and used for the derivation of the quantum kinetic equations. Numerical methods for the solution of the retarded quantum kinetic equations are discussed and results are presented for high-field transport and for mesoscopic transport phenomena. Quantum beats, polarization decay, and non-Markovian behaviour are treated for femtosecond spectroscopy on a microscopic basis. Since the publishing of the first edition in 1996, the nonequilibrium Green function technique has been applied to a large number of new research topics, and the revised edition introduces the reader to many of these areas, such as molecular electronics, noise calculations, build-up of screening and polaron correlations, and non-Markovian relaxation, among others. Connection to recent experiments is made, and it is emphasized how the quantum kinetic theory is essential in their interpretation.