M.C. Chaki's A Textbook of Tensor Calculus is a classic academic resource widely used for upper-undergraduate and postgraduate mathematics, particularly in India.
If you're looking for a verified PDF, I recommend checking online academic repositories, such as: tensor calculus mc chaki pdf verified
Since Chaki’s work is a classic, many professors have uploaded lecture notes or scanned chapters based on his curriculum. While you might not always find the entire book as a single "verified" official file, the curated chapters are usually high quality. 3. Internet Archive (Archive.org) The Line Element: $ds^2 = g_ij dx^i dx^j$