The development of the tensor calculus

The general theory of relativity can only be formulated with the help of tensor calculus. Einstein got to know this in 1912 in the form of the absolute differential calculus. Its creator was Gregorio Ricci, who together with Sophus Lie and others succeeded in expanding the theory of differential invariants. The absolute differential calculus fitted the general theory of relativity like a key to a lock: the calculus developed by Ricci in 1884-92 indeed fulfilled exactly the physical concept of general relativity that Einstein developed in 1907-15. Such a fit was only possible because both Ricci within mathematics and Einstein within physics asked comparable questions, namely questions about invariants in special transformations. An attempt is made to trace the historical path as accurately as possible using the sources.