The main textbook for the course is:
Principles of Analysis, by Walter Rudin.
We will also sometimes follow selections from
Undergraduate Analysis, by Serge Lang.
Here are two additional textbooks that cover much the same material with differing emphasis.
Real Mathematical Analysis by Charles Pugh.
Analysis I and Analysis II by Terrence Tao (two books comprising a 1-year course).
Class member's Textbook Folder