  This paper aims to study the notion of $e^*\text{-}\theta$-open \cite{Ozkoc1}
sets and to investigate new properties of this notion. Also, we define a new
type of set, called $e^*\text{-}\theta\text{-}D$-set, via the notion of
$e^*\text{-}\theta$-open set. Moreover, we introduce some new separation axioms
by utilizing $e^*\text{-}\theta\text{-}D$-sets. We obtain many results related
to these new notions. In addition, the notions of
$e^*\text{-}\theta\text{-}$kernel and slightly $e^*\text{-}\theta\text{-}R_0$
space are defined. Some characterizations regarding these new notions have been
obtained. Furthermore, we have given many examples concerning the mentioned
notions. Finally, we not only put forward the definition of $e^*\text{-}R_1$
space but also obtained some of its characterizations.
