  Let $R$ be a finite commutative ring with $1\ne 0$. In this article, we study
the total graph of $R$, denoted by $\tau (R)$, determine some of its basic
graph-theoretical properties, determine when it is Eulerian, and find some
conditions under which this graph is isomorphic to $Cay(R,Z(R)\backslash\lbrace
0\rbrace)$. We shall also compute the domination number of $\tau (R).
