TITLE: Rudin's Principles of Mathematical Analysis or Apostol's Mathematical Analysis?
QUESTION [50 upvotes]: I am in high school and have no access to a professor or anyone. I previously used Calculus Volume I by Tom Apostol and Spivak's Calculus (for the differential calculus bit).
I can choose between  Mathematical Analysis by Tom Apostol and  Principles of Mathematical Analysis by Walter Rudin, as I was gifted Rudin by a friend and ended up buying Apostol as well. I will be indebted if someone told me which one is the tougher one and which one is better for the self-learner.  I have no issues about how tough the book is, but I would like  the book that enables me to understand the subject better without being too compressed or too verbose and guides me better.

REPLY [3 votes]: You can try "Curso de análise" vol1 and vol2 by Elon Lages Lima too
In this series of books ideas under a topological analysis approach and to some extent intuitive occur . It is harder to read than Apostol but less than Rudin, the problems are not easy so working on them will help to absorb the ideas of analysis.

Vol 1 here
Vol 2 here 
Vol 3 here