[asknthrow2020]

For analysis you absolutely MUST read Principles of Mathematical Analysis by Walter Rudin. Covers everything and is literally a gold standard text in modern analysis. "Baby Rudin" is essentially the analysis bible that all subsequent texts worked off of.

[mennis16]

I heard a bunch of students complain about how tough the text for our Real Analysis class was, so I was surprised to find it felt pretty readable to me. Turns out it was a new prof that semester who decided to go with "Mathematical Analysis, Second Edition by Tom Apostol" instead of Baby Rudin.

Point being, there may be a better analysis text for this student to start with right now- depends highly on their background/situation, but personally I am glad I didn't have to read Rudin for my first "real" math course.

[rokobobo]

Seconded. For what it's worth, Harvard's Math 55 uses that as its textbook.