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Tullio Levi-Civita (1873-1941) gave remarkable contributions to several mathematical and physical fields – such as hydrodynamics, the three-body problem, differential geometry and general relativity. In 1900 he published together with Gregorio Ricci Curbastro the famous paper “Méthodes de calcul differential absolu et leurs applications” where the absolute differential calculus (nowadays called tensor calculus) is organized in a rigorous and systematic theory. From May to November 1915 he exchanged many letters with Albert Einstein about general relativity, in particular on the gravitational field equations. Levi-Civita strongly developed relevant topics of differential geometry, by introducing for instance the concepts of parallel transport (1917) and geodesic deviation (1927). These works are strictly connected to the general theory of relativity. In this talk we aim at examining the influence of Levi-Civita’s research on the development of differential geometry and tensor calculus , in connection to physics. In this context, we analyse the complexity and peculiarity of Levi-Civita’s international school at the University of Rome by using the unpublished documents kept in Levi-Civita’s Archive at the Biblioteca dell’Accademia dei Lincei in Rome.

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