I know there looks to be a duplicate:
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)