The Absolute Differential Calculus (Calculus of Tensors) - Dover Mathematics Book | Tensor Analysis for Physics & Engineering Applications

Although it is a bit dated, this is a wonderful book by the one of the main instigators of Tensor Calculus. I would like to stress however as others have noted that it is quite difficult material, but that is the case with most forms of upper division mathematics. The coverage of Classical mechanics is a bit sparse and nothing of electrodynamics is considered since the author himself states that there is much material that already exploits the usage of Tensor analysis in electromagnetism. Nevertheless the treatment of General Relativity is quite complete. For those interested in Tensors, this is one of the main books to have. Those with knowledge of Multivariate calculus and linear algebra should be able to fly through the introductory chapters. After this book, I suggest Eisenhart and Einstein's paper on the General theory as ways to venture the wonderful world of tensors.Interestingly enough I have also heard that Tensors are being superseded by "functors." But, as is the case of physics and mathematics, one cannot plunge into the abyss of contemporary knowledge without some notions from the past.