I know there looks to be a duplicate:

What are the prerequisites to studying general relativity?

From what I read, the prerequisites are Calculus, linear algebra, differential and partial differential equations, analysis, differential geometry, forms, tensors.

My background right now is Vector calculus, linear algebra (rigorous treatment), complex analysis, differential equations, some basic partial differential equations and basic tensor analysis.

My question is, what prerequisites do I need for these prerequisites, like, to understand manifolds, do I have to study point set topology, group theory, ring theory, algebraic topology, and geometrical topology and all that abstract stuff? And what exactly do I need to understand the idea of differential forms?

I'm looking to buy the topology book by Munkres and learn the whole point set topology from it, do I have to go that far?

Then I'm looking to buy the "Manifolds and Differential Geometry" by Lee, and I also have no idea how far do I have to go, I mean I don't know how far do I have to go in the math of every prerequisite for general relativity.

In short, my goal is to understand general relativity mathematically, I want to be motivated and know where everything comes from in the process so I can comprehend what is going on.

Can anyone guide me through the steps I have to take to develop the math correctly? Oh and also after making sure I'm familiar with all that math, I think I'm going to read "A first course in general relativity" by Shutz.

edit: My physics background is: Griffiths' level E&M, Classical mechanics (Hamilton's principle), Quantum mechanics I, Special relativity (non-tensor formulation)

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    $\begingroup$ Relevent : i.stack.imgur.com/I7nL3.jpg $\endgroup$ – Slereah Dec 11 '19 at 10:23
  • $\begingroup$ It's a struggle. :-( $\endgroup$ – khaled014z Dec 11 '19 at 10:26
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    $\begingroup$ Schutz's book is good if you're after a general feel of how GR works i.e. the basics of what a metric is and how to use it. However if you are interested in a mathematical treatment I would not recommend Schutz. You'd be better off with a book like Carroll's. $\endgroup$ – John Rennie Dec 11 '19 at 10:32
  • $\begingroup$ I'd weigh in that you don't really need to know much/any point set topology to study manifolds. It will help of course, but a typical point set topology course contains way more than you need for this. $\endgroup$ – jacob1729 Dec 11 '19 at 10:37
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    $\begingroup$ You don't need any more prerequisites, just look for a textbook that explains differential geometry also - at the introductory level it is simple extension of ordinary calculus and vector algebra. F.e. you can pick Gravitation by Misner, Wheeler, Thorne right away and you will perhaps find you already know more math than is needed. In this way, you will find yourself which parts of the theory you want to learn better. Also, i was learning differential geometry from Fecko at high school, without ever hearing of words like algebraic topology and i was able to follow (more or less). $\endgroup$ – Umaxo Dec 11 '19 at 14:02