Let $d\ge 1$, and let $F$ be finite subset of $\mathbb{Z}^{d}$.
The set $F$ is called a tile if $\mathbb{Z}^{d}$ can be expressed as a countable disjoint union of translates of $F$. In these talks we will focus on the decidability problem for such tilings, and prove that the question whether a given finite set $F\subset \mathbb{Z}^{2}$ tiles $\mathbb{Z}^{2}$ is decidable.
