What are the pre- requisites required to learn Real Analysis? I already have quite a solid foundation in Single and Multivariable calculus. But how do I know if I'm prepared to tackle real analysis?
Before I get into Real Analysis, I want to know everything that I need to know first. Reading a book, but having to look up sources on the basics that I missed, is a complete waste of time.

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*Please advise me on everything that I need to know before studying Real Analysis.


*Please outline what to expect from Real Analysis, and recommend textbook for beginners.
 A: Well a "solid" background in single variable and multi-variable calculus should be more than enough for you to make an attempt at learning Real Analysis. I have a very feeble foundation on multi-variable calculus but have taken a decent first semester calculus course and am not finding it difficult to make progress studying Real Analysis on my own. I did similar research not so long ago. Here's what I have to tell you. 
I don't know if you have taken a properly rigorous pure mathematics course before. I don't consider first year calculus units to be properly rigorous. Maybe a tiny Abstract Algebra course or a good Linear Algebra course will hone your logical foundations. And this is pretty much all you actually need. A good understanding of mathematical logic - How to negate complicated statements, how to draw direct implications, contradictions, a good idea of what lies beneath a statement, identifying implicit assertions - is all you need in my opinion. 
And this is my humble suggestion. You will not get a proper grasp on a subject like Analysis by reading just one book. You should constantly look for other sources. You will have to do this for example when you read the Basic Topology chapters. Topology does not count as a pre-requisite for Analysis because let's face it that does not make sense. So I suggest you look through multiple books, notes, videos and articles in your way through Analysis. It is a a vast area. No book contains everything. There are various approaches to the subject each with its own merits. Here are some books that I have skimmed through and I think I've ordered them according to difficulty. Maybe someone more competent can verify that. 


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*Stephen Abbott - Understanding Analysis (2001)

*Robert S. Strichartz - The Way of Analysis (2000)

*Yet Another Introduction to Analysis - Bryant (1990)

*William R. Wade - Introduction to Analysis (2004)

*Robert G. Bartle - The Elements of Real Analysis, Second Edition  (1976)

*Real Mathematical Analysis by Charles Chapman Pugh (2002)

*Rudin, W. - Principles of Mthematical Analysis (1976)


The last one is the Golden Standard Text for a first course in Analysis. I preferred Bartle although I believe many would question my choice. Each one of these are very good texts with their own unique merits. You should skim through them and choose the one most suited to you. Good Luck with your studies. 
PS: Maybe you should look here and here for more references. 
