  For an ordered subset $S = \{s_1, s_2,\dots s_k\}$ of vertices and a vertex
$u$ in a connected graph $G$, the metric representation of $u$ with respect to
$S$ is the ordered $k$-tuple $ r(u|S)=(d_G(v,s_1), d_G(v,s_2),\dots,$
$d_G(v,s_k))$, where $d_G(x,y)$ represents the distance between the vertices
$x$ and $y$. The set $S$ is a metric generator for $G$ if every two different
vertices of $G$ have distinct metric representations. A minimum metric
generator is called a metric basis for $G$ and its cardinality, $dim(G)$, the
metric dimension of $G$. It is well known that the problem of finding the
metric dimension of a graph is NP-Hard. In this paper we obtain closed formulae
and tight bounds for the metric dimension of strong product graphs.
