Reddit reviews Contract Theory (The MIT Press)

There is some material in MWG that is considered mechanism design. Chapters 13, 14, 21, 23, maybe some elements in others.

For Contract Theory, this is a great introduction and this is a slightly more advanced followup.

For Matching, this is a good introduction to the basics.

I don't have a good idea for a text for Voting. It's mentioned in MWG to some extent.

If you want seminal papers, these books provide citations of those, as well as many, many others.

A few others have mentioned Mas-Colell, Whinston, and Green's Microeconomic Theory. Personally, I would never recommend that someone read it as a first reference, but it is the most comprehensive book on microeconomics, and can serve as an excellent reference manual that can clarify concepts you come across in your other readings.

There are much better texts (though less comprehensive) than MWG that focus on specific subtopics of microeconomics, for example:

Contract Theory(covers Moral Hazards, Asymmetric Information, optimal wages etc)

General Equilibrium-Overlapping-Generations, optimal growth (covers micro-foundations of macroeconomic theory)

Primer on Game Theory

For macroeconomics, since you are from a Physics background, I would recommend Recursive Methods in Economic Dynamics.

Edit: One "popular" book I read that I found to be fairly decent on economic theory was "The Ascent of Money" by Niall Ferguson