  We introduce the fundamental group $F(\mathcal{M})$ of a finite von Neumann
algebra $\mathcal{M}$ with finite dimensional normal trace space. The form of
$F(\mathcal{M})$ is completely determined. Moreover, there exists a finite von
Neumann algebra $\mathcal{M}$ with finite dimensional normal trace space such
that $F(\mathcal{M})=G$ for any conceivable groups $G$ as fundamental group.
