The Fourier Algebra for Locally Compact Groupoids We introduce and investigate using Hilbert modules the properties of the {\em Fourier algebra} $A(G)$ for a locally compact groupoid $G$. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a special case the classical duality theorem for locally compact groups proved by P. Eymard. Keywords:Fourier algebra, locally compact groupoids, Hilbert modules,, positive definite functions, completely bounded mapsCategory:43A32