Real Analysis Textbooks

[unitroot]

I like Serge Lang's "Undergraduate Analysis" text. It's very much on the same level with baby Rudin but I think it's more readable and I like the way it dedicates a lot more space to analysis in R^n than other books. It has some interesting theorems, like multivariate Taylor series and Taylor's theorem that are not in many other books.

Pugh's real analysis book is another interesting option. Again it's on the same level with Rudin, but seems more readable, has more graphs, and the section on topology is very good.

[Bargalhao]

Principles of Real Analysis, (along with Problems in Real Analysis, which contains complete solutions to every problem featured in Principles) by Aliprantis and Burkinshaw. THE most underrated Real Analysis book out there. Very clear, precise, and all exercises have solutions, which is a rare feature in any RA book.

[SubEffect]

Yeah, I really liked the Aliprantis as a companion to my normal real analysis text. The problems (but mostly the solutions) are extremely helpful in studying for tests, as long as you don't just get lazy and look at the answers immediately. However, I once got lucky with a test question that was exactly the same as one I had already reviewed in Aliprantis...

[waxwings]

What about Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross?

Edit: Hah, never mind. I missed the second page.

[shootermcgavin7]

Originally Posted by unitroot

Pugh's real analysis book is another interesting option. Again it's on the same level with Rudin, but seems more readable, has more graphs, and the section on topology is very good.

Another vote for Pugh.