  A path in an edge-colored graph $G$, where adjacent edges may have the same
color, is called a rainbow path if no two edges of the path are colored the
same. The rainbow connection number $rc(G)$ of $G$ is the minimum integer $i$
for which there exists an $i$-edge-coloring of $G$ such that every two distinct
vertices of $G$ are connected by a rainbow path. The strong rainbow connection
number $src(G)$ of $G$ is the minimum integer $i$ for which there exists an
$i$-edge-coloring of $G$ such that every two distinct vertices $u$ and $v$ of
$G$ are connected by a rainbow path of length $d(u,v)$. In this paper, we give
upper and lower bounds of the (strong) rainbow connection Cayley graphs of
Abelian groups. Moreover, we determine the (strong) rainbow connection numbers
of some special cases.
