Beginner (yet rigorous) book recommendation for differential geometry / topology for General Relativity

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I went through a quite a lot of posts here but did not find the information I wanted. I'm looking for a beginner / introductory (yet mathematically rigorous) book recommendation for differential geometry / topology required for General Relativity.

I'm perfectly fine (in-fact I like) the so-called dry mathematics books (theorem-proof-theorem). What I need is -

  1. Very clear definition of Mathematical objects used in GR
  2. Crisp / rigorous proof in modern notation

I need the book at advanced undergraduate or beginner graduate level. Thanks in advance.