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While Gravitation by M T W is certainly excellent, any introductory Topology textbook would also be helpful. Topology is not something I'm strong in, but I do have a few books. Unfortunately, I'm currently at work, and cannot recall titles.

This falls under the area of General Relativity. If you already have a background in maths, my recommendation would be the book Gravitation by Misner/Thorne/Wheeler.

Avoiding threads with exchanges such as these

<Ant fucking mode> nope, it is 'omniscient' </Ant fucking mode> I am wondering when @Night FM will answer my question.

Though generally speaking, I never really found a meaningful difference on the undergrad level. Perhaps the one thing is that many top programs are able to delay grade inflation more as they have more applicants. Maybe there is more in other disciplines that I am missing.

Of course it is. Germans like to categorize stuff and there is a distinction between applied sciences (which are often called Technische Hochschule) which usually includes areas such areas with applied training such as engineering, nursing etc. and "regular universities.

It really depends on which level you are looking at it. Undergrad? Not so much. There can be differences in how the technical labs are equipped, though in the US (and elsewhere) labs are getting cut because of cost. This trend is less so in countries in which Universities are not funded by tuition. I will also add that having tuition as a significant part of the university budget often creates perverse incentives and often also leads to administrative bloat. Examples include having offices who are actively trying to recruit and attract students, which is largely absent in entirely publicly funded institutions. Likewise, there is more incentive for student retention, which is associated with higher grade inflation. From a student perspective the experience can be better as there is more support (incl. recruitment, accommodation, living space, guidance and career counseling, as well as easier to grieve grades). But it does not mean that the education is better (often the reverse, actually). On the graduate level, that depends more on individual researchers than the university per se. I.e. individual profs can run successful groups regardless on which university they are working in. However, there are disparities between countries. The US provides quite a bit of funding for research, but there are quite differences between European countries. Highly ranked universities are often also flush with money and often support profs more with resources to establish successful research programs. That being said, there are many moderately or low ranked universities with good researchers and successful (research) graduate programs. Things are a bit iffier when the University primarily sees itself as a teaching university. There, Profs struggle to maintain a program as they get virtually no support (e.g. no lab space). They therefore rarely have successful programs in natural sciences (though they might have social science programs).