TITLE: Experiences with Rudin?
QUESTION [15 upvotes]: So I am trying to tutor a friend in analysis. This is her first time with proofs. We are on chapter 2 – the topology chapter – of Rudin's Principles of Mathematical Analysis and she is extremely frustrated, mainly because she expects herself to learn at a more rapid pace than is occurring (although she is doing fine imo). When I was learning the material, I recall Rudin taking a long time, as I presume it was for many first timers. 
So what are you guys' experience with Rudin? How long did you spend on chapter 2? Is there anything that you found useful to help you get through the book? 
I am hoping that if she sees that the math community finds the material/book challenging (assuming you do), she will feel more comfortable.

REPLY [2 votes]: Anyone that can just casually read Rudin's Principles and understand it all without effort is an outlier IMO. For me, sometimes I spend an hour on a single sentence. So the frustration was there for me too but it went away when I set different goals for myself. Initially I wanted to read a certain number of pages in a certain time period - now, I no longer care how long it takes, I see each little proof as an individual accomplishment and a mathematical marvel that deserves to be studied in detail. Completely digesting the material takes a long time but is very rewarding in the end.