  In the present paper we study the representations of the Jacobi algebra. More
concretely, we define, analogously to the case of semi-simple Lie algebras, the
Verma modules over the Jacobi algebra ${\cal G}_2$. We study their reducibility
and give explicit construction of the reducible Verma modules exhibiting the
corresponding singular vectors. Using this information we give a complete
classification of the reducible Verma modules. More than this we exhibit their
interrelation of embeddings between these modules. These embeddings are
illustrated by diagrams of the embedding patterns so that each reducible Verma
module appears in one such diagram.
