Powerful many-body methods are being developed to allow the prediction of macroscopic properties of non-relativistic quantum systems. The approach is based on the use of Feymann diagrams and variational wave functions and is aimed at developing approximation schemes that allow the best possible accuracy for a given computational effort and applying them to realistic systems. The systems of greatest interest are finite nuclei, but the methods will be applied to other interesting many-body systems such as electrons in metals and quantum liquids. These methods offer especial promise for understanding inhomogeneous systems.
