  This work reviews recent advances in the analytical treatment of the
continuum spectrum of correlated few-body non-relativistic Coulomb systems. The
exactly solvable two-body problem serves as an introduction to the
non-separable three-particle system. For the latter case we discuss the
existence of an approximate separability of the long and the short-range
dynamics which is exposed in an appropriately chosen curvilinear coordinates.
  The three-body wave functions of the long-ranged part of the Hamiltonian are
derived and methods are presented to account approximately for the short-ranged
dynamics. Furthermore, we present a generalization of the methods employed for
the derivation of the three-body wave functions to the scattering states of $N$
charged particles.
  To deal with thermodynamic properties of finite systems we develop and
discuss a recent Green function methodology designed for the non-perturbative
regime.
  In addition, we give a brief account on how thermodynamic properties and
critical phenomena can be exposed in finite interacting systems.
