Discover the Basics of Real Analysis: A Gentle Introduction

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For those seeking a gentle introduction to real analysis, "Calculus" by Michael Spivak is highly recommended for its readability and focus on analysis within the real numbers. For a broader approach that includes metric spaces, Hilbert, and Banach spaces, "Foundations of Mathematical Analysis" by Richard Johnsonbaugh and W.E. Pfaffenberger is suggested as an accessible option. Additionally, for those interested in topology, "Introduction to Topology" by Theodore W. Gamelin and Robert Everist Greene is worth considering. "Real Mathematical Analysis" by Pugh is noted as an excellent introductory text, while "Understanding Analysis" by Stephen Abbott is also recommended for its clarity and approachability.
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a gentle intro to real analysis? any suggestions anyone? something very readable?
 
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Calculus by Michael Spivak is a very readable introduction to real analysis-- that is, analysis on R.
If you want something which starts with R and moves onto the more general metric space, Hilbert and Banach space setting though, a very readable (Dover) book is Foundations of Mathematical Analysis by Richard Johnsonbaugh and W.E. Pfaffenberger.
You might also appreciate a book on topology if you're looking for something of the latter category-- I'm currently reading through Introduction to Topology by Theodore W. Gamelin and Robert Everist Greene.
Both books were recommended to me in this thread, so you might want to take a look there as well.
 
Pughs Real Mathematical Analysis is IMO the best introductory analysis book for learning the subject.
 
for anyone else i was recommended understanding analysis by stephen abbott
 

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