While you search for a free PDF, understand that the official updated material is often found in the Cambridge University Press companion website. This site includes:
Leonard Susskind’s approach to General Relativity (GR) in The Theoretical Minimum is distinct from traditional textbooks. Rather than starting with the obscure history of the equivalence principle or the bending of light, Susskind and Cabannes focus immediately on the mathematical machinery required to describe gravity: Riemannian Geometry and Tensor Calculus.
Here is the developmental arc of the subject as presented in the text. the theoretical minimum general relativity pdf upd
Fix: The upd edition adds a margin note: "τ is what your wristwatch reads; t is what a distant observer's clock reads." Rewrite every equation in terms of d/dτ.
Many online forums (Physics StackExchange, r/PhysicsStudents) posted corrections for problem #3 in Chapter 4 (Gravitational Redshift). The updated edition has renumbered and reworded that problem. While you search for a free PDF, understand
Bottom line: If you are learning GR for the first time, the original edition will actively confuse you. You need the upd version.
Theory is useless without solution. The book concludes by solving the field equations for the simplest non-trivial case: a spherically symmetric mass (like a star or a black hole) in a vacuum. Fix: The upd edition adds a margin note:
The result is the Schwarzschild Metric: $$ds^2 = -\left(1 - \fracr_sr\right)dt^2 + \left(1 - \fracr_sr\right)^-1dr^2 + r^2 d\Omega^2$$
This solution predicts: