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The standard grad school text these days for dynamic macro is Ljungqvist & Sargent's Recursive Macroeconomic Theory. You won't need to go through the whole thing necessarily, but to be able to tackle the Woodford book, I would think chapters 1-4, 7-8, 12-13, 16-17 and 24-26 would be quite helpful.

There's also Simon & Blume's Mathematics for Economists, which is a good reference book should you need it. For example, the discussion and motivation of Lagrange multipliers and the Kuhn-Tucker optimization conditions is very good.

One noteable omission from both of those books which you will likely encounter at some point is continuous-time optimization/optimal control. This topic is often covered in the appendices of various grad-level macro textbooks, but perhaps the best I've come across is Chapter 7 of Daron Acemoglu's Introduction to Modern Economic Growth. The appendix to Barro & Sala-i-Martin's Economic Growth also has some pretty good coverage.

By the way, if you hunt around, all of these textbooks can be found online for "free".

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

If you are interested in books that read as generic non-fiction books and not as textbooks, these two were interesting to me and assigned by professors (one of my majors was economics).

The Choice by Russell Roberts is a very accessible text about international trade (so this book will definitely drive home how free trade is best for society as a whole) but its themes are relevant to general economic theory as well. It is written in the form of Platonic conversation where the entire story is just two people talking back and forth in a question:answer format. My macro professor made all of his classes read it, even his honors students.

The Ultimate Resource 2 by Julian Lincoln Simon explores issues of resource scarcity, population dynamics, and technology diffusion; each of these is important to economic theory and the themes and anecdotes explored here are common to economics. Some of the ideas expressed might fall more into the Austrian/Libertarian camp, but certainly not all (it isn't always black-and-white).

Thank you, what is your opinion of Schumpeter. Many seem to like it as well. But sir, that is exactly what I am looking for. Simply put, as of right now, I am reading blogs and sometimes their references escape me, such as Scott Sumner frequently referencing "The Money Illusion," which I guess is to be expected, and other models that are not familiar to me. So although the models and text may be outdated, they are still referenced in areas I do not yet understand. But thank you for your help.

non-Austrian economics is not a 'type' of economics - rather, the normal economics sub-reddit became swamped with adherents of this basically completely fringe quasi-philosophical, very political, and anti-scientific Austrian 'economics'. The wiki article for it is quite charitable. Basically you can discount about half of all comments in the main subreddit right off the bat.

Trying to think of non-text-books, not-too-mathematical books that are general in scope, fun to read, and minimise politicking...difficult

John McMillan, Reinventing the Bazaar - explanation of the limits and power of markets with many examples

Todd Buchholz, New Ideas from Dead Economists: An Introduction to Modern Economic Thought - a sort of history of economists with a heavy emphasis on their thoughts and contributions using real world examples to illustrate

William Breit and Barry T. Hirsch, Lives of the Laureates - essays by many of the most highly-acclaimed recent economists mostly sort of mixed idea and personal life stories.

Hope these help. Have fun.

I haven't read this book yet but it looks like it summarizes the findings of Baumol and Gomory.

Also, I wish I could have found a better review, but at least this one gives you a feel for the content of the argument.

There are lots of good recommendations on the technical side, (also, this for game theory and this is excellent intro into econometrics), but most economic insights are really very simple, and if you want to practice these ideas, I recommend blogs. These two are my favourite general blogs:

Marginal Revolution

Modeled Behaviour

This is the first essay from found in Fluttering Veil by Leland yeager. I'm still not done reading through all of the book, but it's really damn good. I highly recommend it.

Harbo's got the textbooks covered, though I'd recommend Romer's Advanced Macro instead of Sargent and Ljungqvist. I like this book for something that's less technical but covers a lot of the current research and thinking in the field.