H.L. Royden's Analysis was a book that made real analysis click when I read it on my own time in High School. It's simple enough so an intelligent kid can read it and think that simplicity can allow a solid understanding that some people can miss reading more sophisticated book.
It's also true that being forced to really work at a problem, whether by a class or a job, can also be invaluable way for concepts to click. Facing a problem that doesn't budge with your habitual approach forces you to try backing up and looking from a wider perspective as well as working at the problem with greater exactness and attention.
H.L. Royden's Analysis was a book that made real analysis click when I read it on my own time in High School. It's simple enough so an intelligent kid can read it and think that simplicity can allow a solid understanding that some people can miss reading more sophisticated book.
It's also true that being forced to really work at a problem, whether by a class or a job, can also be invaluable way for concepts to click. Facing a problem that doesn't budge with your habitual approach forces you to try backing up and looking from a wider perspective as well as working at the problem with greater exactness and attention.