In this talk,  after recalling basic facts on groupoids, we will see that the structure of a groupoid G is entirely determined by giving invariant subsets by cyclic permutations of the Cartesian product G^k for k=0,…,3 and satisfying some additional properties.  We will then focus our attention on a special type of groupoids, namely VB-groupoids and see how this point of view allows to find very simply the construction of the dual groupoid of a VB-groupoid. In particular, we recover the famous Weinstein’s cotangent groupoid. Finally, we will construct a Fourier transform in this situation which induces an isomorphism between the C*-algebra of a VB-groupoid E and the  C*-algebra of the VB-groupoid dual E*.This is a work in progress with Georges Skandalis.