The official source for notes is Susskind’s personal Stanford page. Look for the file usually named GR_Lecture_Notes.pdf .
If you are learning GR for the first time, the original edition will actively confuse you. You need the upd version. the theoretical minimum general relativity pdf upd
The original text had a confusing step when deriving the geodesic equation from the Lagrangian. The updated version adds an intermediate line showing how δ∫ g_μν dx^μ dx^ν = 0 leads to the Christoffel symbols. This is crucial for beginners. The official source for notes is Susskind’s personal
Sample blurb for the PDF front matter "This concise introduction presents the minimum theoretical and mathematical background required to begin doing calculations in general relativity. Emphasizing intuition and worked examples, the text guides the reader from special relativity through metric geometry to Einstein's equations and important exact solutions." You need the upd version
The theoretical minimum culminates in the "action" principle. Just as Newton gave us $F=ma$, Einstein gave us the relationship between geometry and matter.