  Low dimensional spin-1/2 systems with antiferromagnetic interactions display
very innovative features, driven by strong quantum fluctuations. In particular,
geometrical effects or competing magnetic interactions can give rise to the
formation of a spin gap between the singlet ground state and the first excited
triplet state. In this chapter, we focus on the numerical investigation of such
systems by Exact Diagonalisation methods and some extensions of it including a
simultaneous mean-field treatment of some perturbative couplings. After a
presentation of the Lanczos algorithm and a description of the space group
symmetries, we give a short review on some pure low-dimensionnal frustrated
spin gapped systems. In particular, we outline the role of the magnetic
frustration in the formation of disordered phase. A large part is also devoted
to frustrated Spin-Peierls systems for which the role of interchain couplings
as well as impurity doping effects has been studied numerically.
