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I am now going through Isham's book Modern differential geometry for physicists and got stuck with the notions of etale bundle, presheaf and sheaf. Could someone please suggest some other, more intuitive and more accessible references on etale bundles and sheaves, preferably the ones giving more motivation and sufficiently many explicit (and worked-out) examples and, preferably, accessible to theoretical physicists (i.e., not just mathematicians)?

P.S. To make things clear, a few math texts I have managed to find so far like Godement's and Bredon's Sheaf Theory (two books with the same title) seem way too tough for me. The part on sheaves in Arapura's Algebraic Geometry over Complex Numbers is somewhat better but still a bit too fast going and with too few examples and not too much motivation. Pretty much the same applies to the part on sheaves (which is too brief anyway) in the Clay Institute volume Mirror Symmetry. If there are no suitable books, are there perhaps some good lecture notes on the subject accessible to physicists rather than just mathematicians, from which one get a reasonable intuition on sheaves and stuff?

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Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!

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Here is a motivation for the general notion of sheaf and sheaf cohomology:

A general introduction to differential geometry as needed in physics in terms of sheaves is at

More along these lines is in section 1.2 of arXiv:1310.7930, which describes physics in terms of sheaves (and higher sheaves) on smooth manifolds (and variants thereof).

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