Summary: Let \(G\) be a graph with no isolated vertex. A set \(D\subseteq V(G)\) is a total dominating set of \(G\) if every vertex of \(G\) is adjacent to at least one vertex in \(D\). The total domination number of \(G\), denoted by \(\gamma_t(G)\), is the minimum cardinality among all total dominating sets of \(G\). In this paper we study the total domination number of total graphs \(\texttt{T}(G)\) of simple graphs \(G\). In particular, we give some relationships that exist between \(\gamma_t(\texttt{T}(G))\) and other domination parameters of \(G\) and of some well-known graph operators on \(G\). Finally, we provide closed formulas on \(\gamma_t(\texttt{T}(G))\) for some well-known families of graphs \(G\).