The theory of Inversion presents one of the simplest examples of those Birational Transformations of plane figures, whose general theory is due to Cremona. It has a distinguishing feature to which it owes its name. If the point P “inverts” into Q, then Q inverts into P. It is therefore a simple case of these involutive point transformations much of the general theory of which was developed by the late Admiral de Jonquières in a paper printed as late as 1864 in the Nouvelles Annales, but which had originally been addressed to the Institute of France in 1859. This memoir is not only highly interesting, but is eminently readable and very ingenious.