This manuscript expands on class notes developed for a 10-week course on general relativity, which follows a first course on differential forms. It is intended either as a textbook for a mathematics topics course, and/or for reference. The manuscript emphasizes the use of differential forms, rather than tensors, which are barely mentioned. The focus is on the basic examples, namely the Schwarzschild black hole and the Friedmann-Robertson-Walker cosmological models. The material should be suitable for both advanced undergraduates and beginning graduate students in both mathematics and physics. The subject is treated as advanced vector calculus, rather than analysis; the only prerequisites are vector calculus, linear algebra, and a modicum of mathematical sophistication — and that first course in differential forms.
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