Let $G = (V, E)$ be a simple graph with no isolated vertices and $p\geq 3$. A set $D\subseteq V$ is a dominating set, abbreviated as $DS$, of a graph $G$, if every vertex in $V-D$ is adjacent to some vertex in $D$, while a total dominating set, abbreviated as $TDS$, of $G$ is a set $T\subseteq V$ such that every vertex in $G$ is adjacent to a vertices in $T$. A set $T$ is a superlative total dominating set, abbreviated as $STDS$, of a graph $G$ if $V - T$ is not contains a $TDS$ but it contains a $DS$ of $G$. The superlative total domination number $\gamma_{st}(G)$ is the minimum cardinality of a $STDS$ of a graph $G$. In this paper, we initiate a study on $\gamma_{st}(G)$ and its exact values for some classes of graphs. Furthermore, bounds in terms of order, size, degree and other domination related parameters are investigated.