[hgsgm]

I used Rudin in school. I got the highest grade in my class that included several future PhDs and professors. It's an old, not very good pedagogical book. It's a useful reference, if you are living in the pre+Internet, pre color-illustration, mid 20th century. I learned analysis mainly from the guidance of my amazing professor (a postdoc who was an enthusiastic caring, clear communicator).

Like most textbooks, Rudin it has focused exercises, examples to build intuition, and proofs with little steps removed, not free-range problems. Thebanswe to a problem is based on the 20 previous pages in the text.

How to Solve It is like advice for solvimg a jigsaw puzzle (edges first, sort by shape and color and texture, ...) It is for solving problems after you've learned a whole year(s) of material, and don't know which of your knowledge contains the pieces of the answer. It's a way of searching through your knowledge and evaluating which pieces are useful for the problem at hand, and how they fit together.