  Let $G=(V,E)$ be a graph and $P\subseteq V$ a set of points. Two points are
mutually visible if there is a shortest path between them without further
points. $P$ is a mutual-visibility set if its points are pairwise mutually
visible. The mutual-visibility number of $G$ is the size of any largest
mutual-visibility set. In this paper we start the study about this new
invariant and the mutual-visibility sets in undirected graphs. We introduce the
mutual-visibility problem which asks to find a mutual-visibility set with a
size larger than a given number. We show that this problem is NP-complete,
whereas, to check whether a given set of points is a mutual-visibility set is
solvable in polynomial time. Then we study mutual-visibility sets and
mutual-visibility numbers on special classes of graphs, such as block graphs,
trees, grids, tori, complete bipartite graphs, cographs. We also provide some
relations of the mutual-visibility number of a graph with other invariants.
