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**Summary:**At this point, I am thorough with single variable, multivariable calculus, differential equations, linear algebra and basic concepts of point-set topology and tensor analysis. To learn General Relativity along-with its mathematical rigor, what are the topics I should first be thorough and in what order should I learn them?

I am currently studying as a second year undergraduate. I am, along-with my professors, planning to organize a lecture series to be lectured by me on General Relativity. I would personally like the lecture to include the mathematics of the topic rather than it being superficial. The lecture series is going to be organized in January next year so I have about three months at hand. But at this point I am thorough with only those topics I have mentioned in the summary. What more topics should I learn before starting to learn GR? Also in what order should I learn them so as to understand each topic thoroughly?