TITLE: Companions to Rudin?
QUESTION [17 upvotes]: I'm starting to read Baby Rudin (Principles of mathematical analysis) now and I wonder whether you know of any companions to it. Another supplementary book would do too. I tried Silvia's notes, but I found them a bit too "logical" so to say. Are they good? What else do you recommend?

REPLY [4 votes]: Okay, so as you haven't accepted any of the answer, I thought maybe I should give a try to answer as best as I can.      
I'm currently doing Chapter-3 from Walter Rudin's text, and simultaneously following these wonderful notes, https://www.math.ucdavis.edu/~emsilvia/math127/math127.html  by UC,Davis.
       They include proof of each and every theorem and lemma in the book, and even a statement that is left in the book for the readers to prove is proved in these notes.       
If you want, you can follow only these notes and not do theory from the book at all, and directly come back to it to solve problems at the end.