In these proceedings basic questions regarding n-body Schr|dinger operators are dealt with, such as asymptotic completeness of systems with long-range potentials (including Coulomb), a new proof of completeness for short-range potentials, energy asymptotics of large Coulomb systems,asymptotic neutrality of polyatomic molecules. Other contributions deal withdifferent types of problems, such as quantum stability, Schr|dinger operators on a torus and KAM theory, semiclassical theory, time delay, radiation conditions, magnetic Stark resonances, random Schr|dinger operators and stochastic spectral analysis. The volume presents the results in such detail that it could well serve as basic literature for seminar work.