I major in macroeconomics. So, it may be a good idea to share my experience, i.e. how I studied (and am studying!) macroeconomics.
If you are new to macroeconomics, you are highly recommended to begin with Mankiw's principles of macroeconomics. You don't see any mathematics in this text, so don't have to worry about math!
After reading principles of macro, you should go either Blanchard's Macroeconomics or Mankiw's intermediate Macroeconomics (I read both, by the way). At this stage, you can say that you are familiar with undergraduate macro and see the world through the lens of macro! Read blogs by macroeconomists: you can understand now. (I read Mankiw and Cochrane every day.)
If you want to continue (i.e. graduate macro), you cannot escape from mathematics. But there are many good textbooks on math for economists. I recommend Dowling's Introduction to Mathematical Economics. This is wonderful and very easy to follow, but covers most math tools you'll need (if time allows, also read Chiang and Wainwright's Fundamental Methods of Mathematical Economics and Chiang's Elements of Dynamic Optimization). I didn't study Math III and Math C at high school, but after reading these three books, I'm really equipped with math tools for (macro)economics.
After mastering most math tools, you want to try either Benassy's Macroeconomic Theory or David Romer's Advanced Macroeconomics. And if time allows, read the classic: Lectures on Macroeconomics by Blanchard and Fischer (mathematically speaking, Benassy is very friendly, Romer is not that diffiicult, and Blanchard-Fischer is very technical). At this stage, you know what macroeconomics is (almost) all about.
Actually, three textbooks above present collection of various macro models. If you want to specialize in one specific topic, you have to look for other materials. In my case, I major in New Keynesian DSGE models. So, I study lecture notes by leaders in this field, Gali, Christiano, and Moll.
FYI:
Leaders in Growth Theory - Acemoglu and Charles Jones (Jones has excellent data on standard of livings across countries!).
Leaders in Computational Macroeconomics - Jesus Fernandez-Villaverde.
Leaders in Macroeconomics - Chris Edmond, Ivan Werning, Michael Woodford, and John Cochrane.
Sorry, but I cannot introduce all...(Google yourself!)
Leaders in Growth Theory - Acemoglu and Charles Jones (Jones has excellent data on standard of livings across countries!).
Leaders in Computational Macroeconomics - Jesus Fernandez-Villaverde.
Leaders in Macroeconomics - Chris Edmond, Ivan Werning, Michael Woodford, and John Cochrane.
Sorry, but I cannot introduce all...(Google yourself!)


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