On the Algebraic Integrals of the Dynamical Equations

We bring to the reader’s attention a translation of Levi-Civita’s work "Sugli integrali algebrici delle equazioni dinamiche" (1896). In this work, Levi-Civita exposes some of its results concerning the first integrals of the Lagrangian dynamical systems, which are rational in the velocities. Of a particular historical interest is the fact that here he introduces the concept of Killing tensor and the Killing equation. The Editorial Board is grateful to Professor Sergio Benenti for the translation of the original Italian text and valuable comments.