It sounds like you’re looking for a comprehensive guide to the book by Charles W. Misner , Kip S. Thorne , and John Archibald Wheeler (often abbreviated MTW ).
Includes differential geometry chapters (8–11, 14) in depth, plus variational principles (Ch. 21). gravitation charles misner
Chapters 1–6, 7–10, 13, 15, 17, 18, 20, 25, 27–29. Goal: Understand black holes, gravitational collapse, and cosmology with minimal math. It sounds like you’re looking for a comprehensive
Adds chapters 9 (geometry of spacetime), 35 (?) – Actually check: modern readers skip to linearized waves. MTW’s Track 2 is for theory & experiment. Kip S. Thorne