A lot of studies have been conducted on dense topological spaces over a long period of time and interesting results have been obtained. Normality and compactness on topological spaces have also been investigated for decades however, characterization when the subspaces are particularly dense has not been exhausted. In the present study, we consider the case when the countable subspaces are dense. We introduce the notion of normality in dense topological spaces Also, some characterizations and properties of these notions are investigated.