Advanced undergraduate(?) Real Analysis book which is concise and lots of interesting problems I have gone through the other book recommendations on Real Analysis, but I think my requirements and background is slightly different. I am a Physics undergrad teaching myself Pure math. My journey is pure math has been highly non-linear. I have studied Groups and Rings (Dummit and Foote), some Commutative algebra (Atiyah and MacD ~3 chapters), and some representation theory(Fulton and Harris). I am looking for a challenging enough book for Real Analysis. It should cover the material in for e.g.baby Rudin, but I am thinking of something more concise but deeper, which has maybe more interesting and difficult problems. 
I have done a course on Real Analysis taught from Bartle and Sherbert (I hope this text is not very unknown), but I wish to revisit the material and learn, maybe upto what a standard math undergrad is supposed to know, and also to develop my problem solving skills.
Please feel free to close down the question.

I like Kolmogorov and Fomin "Introductory Real Analysis" - which gives lots of examples and has plenty of good problems. But I'm not sure what kind of problem you are looking for.
If you are after challenging integrals and limits etc Hardy's "Pure Mathematics" has lots of those. I also think Apostol's Mathematical Analysis has a mix of challenging problems.
