  We introduce the fundamental group $\r{F}(\c{A})$ of a unital $C^*$-algebra
$\c{A}$ with finite dimensional trace space. The elements of fundamental group
are restricted by K-theoretical obstruction and positivity. Moreover we show
there are uncountably many mutually nonisomorphic simple $C^{*}$-algebras such
that $\r{F}(\c{A})=\set{I_{n}}$. Our study is due to the results of fundamental
group by Nawata and Watatani.
