  Numerical exact diagonalization is the ultimate method of choice in order to
discuss static, dynamic, and thermodynamic properties of quantum systems. In
this article we consider Heisenberg spin-systems and extend the range of
applicability of the exact diagonalization method by showing how the
irreducible tensor operator technique can be combined with an unrestricted use
of general point-group symmetries. We also present ideas how to use
spin-rotational and point-group symmetries in order to obtain approximate
spectra.
