In 1943, E. Hewitt introduced the concept of resolvable space, namely a space is called resolvable, if it contains two disjoint dense subsets. V. I. Malykhin introduced the concept of extraresolvability using the existence of a special family \({\mathcal D}\) of dense subsets of a topological space \(X\). It is defined by the following condition: \(D\cap D'\) is nowhere dense for any distinct \(D,D'\in{\mathcal D}\) and the cardinality of \({\mathcal D}\) is greater than the dispersion character \(\Delta(X)\) of \(X\). In this paper, the authors give some useful examples of such a space and some conditions that a space becomes extraresolvable. Every countable space with nowhere dense tightness is extraresolvable. The set of rational numbers is an extraresolvable \(T_2\)-space, but not the set of reals. For example, \(\operatorname {CH}\Leftrightarrow\) every separable metric space with \(\omega< \Delta(X)\leq\) the cardinality of \(X\) is not extraresolvable. Under GCH, there is an extraresolvable topological Abelian group with uncountable dispersion character, and also, there is a compact resolvable space of large size. There are some unsolved problems. One of them: Is there a compact first countable extraresolvable space (in ZFC)? This paper is expected to become basic for researchers of extraresolvability.