This is a translation of "Methodes de calcul differential absolu et leurs applications," by G. Ricci and T. Levi-Civita, Mathematische Annalen, vol. 54 (1900). This memoire is one of the most influential and important in the history of both differential geometry and mathematical physics. For example, it seems to have been the basic document from which Einstein learned the tensor analysis that he used in the creation of General Relativity.
