“Sur la dynamique de l'électron,” published in 1906 in Rendiconti del Circolo Matematico di Palermo, is Poincaré's principal publication dealing with relativity. It is, among other things, of very considerable historical interest. To make it more readily accessible, the contents of this comprehensive paper will be presented, in a modernized version, in three parts that correspond to the three major topics treated in the paper. The first part, presented here, deals with the principle of relativity and the Lorentz group as well as with the action principle of Maxwell-Lorentz systems.