In 1985, A. Casson defined an integer invariant for oriented integral homology 3-spheres by introducing an appropriate way of counting the conjugacy classes of the SU(2)-representations of their group. He proved that his invariant λ_{c}satisfies the following interesting properties :

λ_{c}vanishes on homotopy spheres,

λ_{c}is additive under connected sum,

λ_{c}changes sign under orientation reversal,

a simple surgery formula describes the variation of λ_{c}under a surgery on a knot transforming an integral homology sphere into another one, and,

λ_{c}lifts the Rohlin μ-invariant from