  M. Kontsevich proposed a topological construction for an invariant Z of
rational homology 3-spheres using configuration space integrals. G. Kuperberg
and D. Thurston proved that Z is a universal real finite type invariant for
integral homology spheres in the sense of Ohtsuki, Habiro and Goussarov.
  We review the Kontsevich-Kuperberg-Thurston construction and we provide
detailed and elementary proofs for the invariance of Z. This article is the
preliminary part of a work that aims to prove splitting formulae for this
powerful invariant of rational homology spheres. It contains the needed
background for the proof that will appear in the second part.
