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...