Book or text for an introduction to pseudo differential operators on manifolds.

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What text or book is quite enjoyable to start (anti dummies) in the study of differential operators (and pseudo) on manifolds? I have been studying the Wong book to understand pseudo differential operators and I find it quite educational and enjoyable. Will there be any similar about manifolds? I would like to understand the process of how to go from operators on $\mathbb{R}^n$ to manifolds. That's my goal. Thank you

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You can find this material in resources such as Michael Taylor's PDE II book, Hormander III (not exactly fun), these notes by Peter Hintz: https://math.mit.edu/~phintz/files/18.157.pdf, and many more. For a semiclassical approach, see Zworski's book or the newer book by Dyatlov and Zworski (the former author has a pdf version on their website: http://math.mit.edu/~dyatlov/res/res_final.pdf). Dyatlov also has some summarized notes here: http://math.mit.edu/~dyatlov/semisnap/ (see "Monday Aug 5").

The general idea is that a pseudodifferential operator on a manifold should "look like" a pseudodifferential operator in local coordinates. This needs some care, though (one gets a larger class than desired if no growth restrictions are placed on the Schwartz kernel). The above make this much more precise.