  A set of vertices $S$ resolves a graph $G$ if every vertex is uniquely
determined by its vector of distances to the vertices in $S$. The metric
dimension of $G$ is the minimum cardinality of a resolving set of $G$.
  Let $\{G_1, G_2, \ldots, G_n\}$ be a finite collection of graphs and each
$G_i$ has a fixed vertex $v_{0_i}$ or a fixed edge $e_{0_i}$ called a terminal
vertex or edge, respectively. The \emph{vertex-amalgamation} of $G_1, G_2,
\ldots, G_n$, denoted by $Vertex-Amal\{G_i;v_{0_i}\}$, is formed by taking all
the $G_i$'s and identifying their terminal vertices. Similarly, the
\emph{edge-amalgamation} of $G_1, G_2, \ldots, G_n$, denoted by
$Edge-Amal\{G_i;e_{0_i}\}$, is formed by taking all the $G_i$'s and identifying
their terminal edges.
  Here we study the metric dimensions of vertex-amalgamation and
edge-amalgamation for finite collection of arbitrary graphs. We give lower and
upper bounds for the dimensions, show that the bounds are tight, and construct
infinitely many graphs for each possible value between the bounds.
