As we have seen (see Chap.  5), classifications cannot be reduced to the classic representations of Barbut and Monjardet (Ordre et classification, algèbre et combinatoire, vol. 1, Librairie Hachette, Paris, 1970) or of Lerman (La classification automatique, Paris, 1970; Classification automatique et analyse ordinale des données, Dunod, Paris, 1981). Note, however, that Lerman (La classification automatique, Paris, 1970, 73) has proposed to extend partitions search's algorithms to covering problems. A more recent reference on the subject is (Alpert and Kahng in Integr. VLSI J. 19(1–2):1–81, 1995. It is obvious that these representations are not sufficient for describing k-classifications proposed by Jardine and Sibson (Math. Biosci. 2:465–482, 1968). But as soon as we admit overlapping classes, classifications are no more chains of partitions. They are made of covers. So we define first this notion (Sect. 6.3), count the number of covers on a set (Sect. 6.4), study the set of all covers on a set (Sect. 6.5) and the lattice of all minimal covers (Sect. 6.6). It appears that, when the generalized classifications still keep a hierarchic form, they are in fact chains of covers (Sect. 6.7). Now, as we shall see, if those covers are not complete ones, classifications become chains of parts of covers. And as a part of a cover is just the same a part of a partition, i.e. a class, such classifications are just chains of classes (Sect. 6.8). As the lattice of minimal covers does not contain all possible generalized classifications, and as the set of all covers over a set is not a lattice, we are necessarily led to introduce topological notions (Sect. 6.9), because topological relations are the only relations that subsist on this kind of classifications. We can then apply to classifications some basic theorems of topology: first, it is a useful way to get information on them (Sect. 6.10); but, more generally, it is possible to develop a topological representation of information (Haouas et al. in J. Appl. Sci. 8(20):3743–3747, 2008). Finally, those systems of classes happen to be a kind of hypergraphs, so, it appears that the language of relational structure (Sect. 6.11) is the more convenient to describe those structures.