Microeconomics
Beginner: Hidden Order: The Economics of Everyday Life by David Friedman.
Intermediate: Intermediate Microeconomics: A Modern Approach by Hal Varian.
Advanced: Microeconomic Analysis by Hal Varian.
Macroeconomics
I would avoid macroeconomics until you grok microeconomics (and maybe even then), but if you must read something, read Macroeconomic Patterns and Stories by Edward Leamer.
Varian's Intermediate Microeconomics is good. I haven't read Microeconomic Analysis which is apparently more advanced.
The reason I found Varian useful is that principle is paired with math; fairly rigorously up until the later chapters. I also read Mankiw's Principles of Economics, but you don't finish that book able to do any economic number crunching.
On the math side it's mainly differential calculus and algebra. If you have a base there already I suspect it will actually be easier and quicker to absorb the principles from a text with math - since they derive from it.
I would like to learn more about economics but I don't know where to start. Can lesswrong suggest specific areas of economics that are particularly useful for understanding and optimising the world? Specific suggestions such as reading lists and resources would also be much appreciated.