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

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.
