Given \(\Omega,\Lambda\subseteq \mathbb{R}^d\) we say that \(\Omega\) tesselates \(\mathbb{R}^{d}\) with \(\Lambda\) if the copies \(\Omega+\lambda\) with \(\lambda\in\Lambda\) do not overlap and they cover \(\mathbb{R}^d\).
The paper under review discusses the previous problem in different settings using tools such as the Fourier Transform. It also pays attention to tesselations of the integers (which can be defined in the obvious way from the previous definition) and also to tesselations of the cyclic group.
This is an interesting survey which can be read without problems by non-especialists.