Real Analysis textbook indecision What's the best book to study analysis after finishing Spivak's Calculus? I thought about Rudin's Principles of Mathematical Analysis(Which I guess would be much boring for me, but I don't have it so I can't tell if my supposition is right or not), Stein and Shakarchi's Real Analysis, Terence Tao's Analysis(if you recommend it, tell me which edition is the 'right', please) or Pugh's Real Mathematical Analysis? 
Additional info about my purpose: 
- I tend to seek elegance in proofs. 
- I want to grasp concepts the most deeply possible.
- I don't like books that just jump steps without clear explanation, but I don't like books that are boring(books that focus too much in rigor, in the steps, in the "you can prove it this way". I like rigor and it's what - - - I'm seeking, but sometimes authors make it boring. I don't know if I made me intelligible). 
- However, I want books that make me try to 'rediscover the subject';  mean, books that make me think hard on the subject even before he explains the matter. 
- Books with super hard exercises are welcome. 
 A: Well, if you have to choose between the textbooks that you indicated, I'd go with Rudin.  But here are some extra thoughts. Pugh's textbook has a topological flavor and is great if you intend to delve further into modern dynamical systems; many (I mean, a great many) exercises may be hard to do, even if you think that you are "fodão". Tao's textbook is too wordy, I can't cope with it. Stein and Shakarchi's text is a mixed bag, but with a nice mix; maybe it's just what you want. An alternative to all these textbooks that in the end worked for me was T. M. Apostol, Mathematical Analysis, 2nd ed. Now if you want to really learn measure and integration theory, you can't go wrong with A. E. Taylor, General Theory of Functions and Integration. #ficadica
A: i think real analysis is very tricky subject, and i suggest you some books,such as zorich.here is link http://instructor.sdu.edu.kz/~verbovskiy/Math%20Analysis%201/Zorich1_en.pdf. it covers every aspect of mathematical analysis, that you need for mathematical career.My suggestion would be to not afraid of those tough symbols, because early or lately you will be reading research papers, so it would be better if you get used to it now.in general there is no best book, so find one that works for you.i also think that rudin is ok, just push yourself and study those books that i recommended.happy learning.
