  I review recent work and some new results, performed in collaboration with G.
Sierra, on the Real-Space Renormalization group method applied to quantum spin
lattice systems mainly in spatial dimensions one and two, and to spin ladders
which are somehow in between. The first part of these notes is devoted to
non-interacting systems in 1D and 2D and the role played by the correlations
between blocks. The second part comprises interacting systems in 1D, spin
ladders and 2D using the standard BRG method.
