  For a family of graphs $\mathcal{G}$, the $\mathcal{G}$-\textsc{Contraction}
problem takes as an input a graph $G$ and an integer $k$, and the goal is to
decide if there exists $F \subseteq E(G)$ of size at most $k$ such that $G/F$
belongs to $\mathcal{G}$. Here, $G/F$ is the graph obtained from $G$ by
contracting all the edges in $F$. In this article, we initiate the study of
\textsc{Grid Contraction} from the parameterized complexity point of view. We
present a fixed parameter tractable algorithm, running in time $c^k \cdot
|V(G)|^{\mathcal{O}(1)}$, for this problem. We complement this result by
proving that unless \ETH\ fails, there is no algorithm for \textsc{Grid
Contraction} with running time $c^{o(k)} \cdot |V(G)|^{\mathcal{O}(1)}$. We
also present a polynomial kernel for this problem.
