abstract: Towards the end of the nineteenth century, a young Tullio Levi-Civita gave some relevant contributions to mathematical physics through the use of the tensorial methods elaborated by his master Gregorio Ricci Curbastro in the years 1884-1895. In the present talk, I will particularly discuss Levi-Civita’s papers on the transformation laws between two systems of dynamic equations (1896) and binary potentials (1899), which in actual fact represent the most original and successful applications of absolute differential calculus before the advent of general relativity.