When I was in graduate school, An Introduction to Manifolds by Loring Tu and The Elements of Integration and Lebesgue Measure Robert G. Bartle, neither one used

When I was in graduate school, An Introduction to Manifolds by Loring Tu and The Elements of Integration and Lebesgue Measure Robert G. Bartle, neither one used by courses, helped me immensely when studying for the qualifying exams in the respective subjects. They provided so much clarity over Lee and Royden (if you know, you know) that it was amazing that the subjects weren't actually as difficult as you thought. There are a lot of books like this, but these two stand out to me at the moment.