Weinberg is a beautiful explanation of general relativity. Hawking & Ellis present the most influential examples of spacetime models, and prove the necessity of gravitational collapse under mild physical hypotheses. Unfortunately, in any approach to this subject we have to use some messy tensor calculations. We will
assume at least one course in differential geometry. Ultimately we want to consider quantum field theories using path integrals, so we are forced to set up all of our classical physical theories in terms of Lagrangians and principles of least action.