  The subject of this paper is a Jacobian, introduced by F. Lazzeri,
(unpublished), associated to every compact oriented riemannian manifold of
dimension twice an odd number. We start the investigation of Torelli type
problems and Schottky type problem for Lazzeri's Jacobian; in particular we
examine the case of tori with flat metrics. Besides we study Lazzeri's Jacobian
for Kahler manifolds and its relationship with other Jacobians. Finally we
examine Lazzeri's Jacobian of a bundle.
