Want to learn differential geometry and want the sheaf perspective I would like to learn some differential geometry: basically manifolds, differentiable manifolds, smooth manifolds, De Rham cohomology and everything else that is pretty much part of a course in differential geometry. I do however know some deal of category theory and algebraic geometry, and I would therefore like to learn differential geometry from a more "abstract" (categorical and algebraical) setting. Are there any good books for this? I was able to find a book called "Sheaves on Manifolds" but I don't know if it is a good book for learning the subject (AFAIK, the book might assume prior knowledge of differential geometry) 
/edit/ Or just lecture notes.
 A: I'm learning this stuff myself so take this with a large grain of salt but a commenter on this question suggested Warner, Foundations of Differentiable Manifolds and Lie Groups. 
At a glance it looks like it goes through some of the usual topics but then does the de Rahm theorem using sheaves, so you might get along with it. Apart from Ch.5, though, I'm not sure how different it is from a standard treatment. It's a GTM book with minimal prereqs, and if you already know about sheaves it's probably a fairly gentle read.
I'd be interested to know how those in the know regard this text in relation to (what I take to be) the more usual textbooks.
A: It is a bit late, but a book that fits perfectly with your demands was published after this questions was asked:

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*Name: "Manifolds, Sheaves, and Cohomology"

*Author: Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technische Universität Darmstadt, Germany.

*Springer's Link: https://www.springer.com/gp/book/9783658106324
My opinion about this book is that the author makes a perfectly combination of abstract, topological and geometric flavor in a very gentle way that is not usually seen in advanced texts in differential geometry. Prerequisits are sumarized in the appendices and they are not very ambicious. Another plus point is that Prof. Dr. Torsten Wedhorn's research is focus in algebraic geometry (as far as I know), so you won't have any problems with the way he introduces the ideas.
A: I'll suggest

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*S. Ramanan, Global Calculus. Goes pretty fast through the basics of manifolds and instead focuses on differential operators.

*T. Wedhorn, Manifolds, Sheaves, and Cohomology. I haven't read this book myself (though it sits in my bookshelf), but it might be what you are looking for.

*D. Pedchenko, Lecture notes on the Fundamental Structures of Differential Geometry. This arxiv submission recently caught my eye but it seems to only be chapter 1

