  Let $G$ be a group, $\mathcal{P}_G$ be the family of all subsets of $G$. For
a subset $A\subseteq G$, we put $\Delta(A)=\{g\in G:|gA\cap A|=\infty\}$. The
mapping $\Delta:\mathcal{P}_G\rightarrow\mathcal{P}_G$, $A\mapsto\Delta(A)$, is
called a combinatorial derivation and can be considered as an analogue of the
topological derivation $d:\mathcal{P}_X\rightarrow\mathcal{P}_X$, $A\mapsto
A^d$, where $X$ is a topological space and $A^d$ is the set of all limit points
of $A$. Content: elementary properties, thin and almost thin subsets,
partitions, inverse construction and $\Delta$-trajectories, $\Delta$ and $d$.
