  The Jacobi group is the semi-direct product of the symplectic group and the
Heisenberg group. The Jacobi group is an important object in the framework of
quantum mechanics, geometric quantization and optics. In this paper, we study
the Weil representations of the Jacobi group and their properties. We also
provide their applications to the theory of automorphic forms on the Jacobi
group and representation theory of the Jacobi group.
