Measurable cardinals can be characterized by elementary embeddings of the universe \(V\) into some transitive class \(M\). That such an embedding \(j:V\to M\) is elementary means that \(j\) preserves truth, i.e., for every formula \(\varphi (x_1,\ldots ,x_n)\) of the language of set theory, and every \(a_1,\ldots ,a_n\), the sentence \(\varphi (a_1,\ldots ,a_n)\) holds in \(V\) if and only if \(\varphi (j(a_1),\ldots ,j(a_n))\) holds in \(M\). It turns out that a cardinal \(\kappa\) is measurable if and only if there exists an elementary embedding \(j:V\to M\), with \(M\) transitive, so that \(\kappa\) is the first ordinal moved by \(j\), i.e., the first ordinal such that \(j(\kappa)\ne \kappa\). We say that \(\kappa\) is the critical point of \(j\), and write \(crit(j)=\kappa\). The embedding \(j\) is definable from a \(\kappa\)-complete non-principal measure on \(\kappa\), using the so-called ultrapower construction. Conversely, if \(j:V\to M\) is an elementary embedding, with \(M\) transitive and \(\kappa=crit(j)\), then the set \(U=\{ X\subseteq \kappa:\kappa\in j(X)\}\) is a \(\kappa\)-complete non-principal ultrafilter on \(\kappa\). A measure \(U\) obtained in this way from \(j\) is called normal.