Rudin against Pugh for Textbook for First Course in Real Analysis So as I have said before in a previous question, I am taking a first course in Mathematical Analysis, and I'm quite excited. I just found out though that unlike the other professors at my university, my professor is using Real Mathematical Analysis by Pugh. I thought it was rather strange because I have read from so many places that Rudin's text on the topic is "the bible" of mathematical analysis, and also he is the only professor who doesn't use it. So I was wondering what some of you experienced mathemeticians thought of choosing this book over Rudin? Is this book a little easier to use than Rudin's? I have heard the Rudin is quite rigorous.
Every great book on a particular topic will have things another great book omits. Having seen both Rudin and Pugh, I would say they are both excellent choices for a rigorous course in mathematical analysis. Pugh's book may be easier to understand as Rudin is very terse.

Often what we call the bible is just what has been used for many years by many people, but newer alternatives exist and can be equally awesome too.
There are flaws s Rudin book. Taylors theorem is not handled nicely.
differential forms are rather messy. implicist inverse not covered very nicely.
i would say pugh offers lot of insights. but the exercies are quite hard and measure theory is not good. stokes theorem is not complete. implict and inverse function theorem are good but he should offered  general proof in final paragraph which he has left to exercises  dieuodennes foundations is classic
Bartles elments of realanalysis is a very good bookand easier bt implict inverse are not well handled.
langs ntroduces even distributions.book on undergraduate analysis is good and some insights are givem . some thorems are proved in two different ways at different places and comments that interchange order of integration and differentiation under integral sign are corelated. treatment of differential forms is excellent.