Use the PDF’s searchability to your advantage. In physical books, looking up the "Ricci identity" requires flipping. In a PDF, you type the term and find every occurrence. Bookmark Chapter 5 (Covariant Differentiation) and Chapter 7 (Curvature) immediately.
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Moving from algebra to calculus, the book introduces the machinery needed for differential geometry. Use the PDF’s searchability to your advantage
Let us address the elephant in the room. The search term is often a euphemism for a pirated, scanned copy of the book. While the original print edition was published in 1988 (ISBN 978-0070334847), it is currently out of print from major distributors for some regions, though used copies are available. though used copies are available.