A good book for metric spaces? I'm looking for a book to study metric spaces. Two years ago, I used a book written by Burkill. While using multiple topological concepts, I studied Munkres (chapters 2, 3, 4, 5, 6 & 9). I do not feel as comfortable in group theory, ring theory or general topology, so I feel that books such as those written by Hungerford, Robinson, and Atiyah and Mcdonald have been very important in my education. But I have not had that feeling with any book of analysis / metric spaces. I feel that my knowledge in this area is still very basic. What book would you recommend to study analysis?
 A: Good introduction to Metric Spaces Metric Spaces: Iteration and Application
A: Rudin, Principles of Mathematical Analysis.
A: There is a wonderful short book by Kaplansky called Set Theory and Metric Spaces. 
How good is it?  I was able to read it at the beginning of my undergraduate career, and in the intervening years of undergraduate study, graduate study and then mathematical research, I have only ever turned to other books on either of these subjects out of idle curiosity: everything I have ever needed to know is in Kaplansky's text.  
A: Dieudonné's Foundations of modern analysis Chapter 3 is a very thorough treatment of metric spaces. It's a bit dry, but perfect as reference.
A: $Spaces$ by Tom Lindstrøm. It’s a new book and is published by the AMS, but it’s $\textbf{very}$ good. Chapter 3 covers metric spaces. Chapters 4, 5, 6, 7, 8, and 9 cover spaces of continuous functions, normed spaces and linear operators, calculus in normed spaces, measure and integration, constructing measure, and Fourier series, respectively. (Of course baby Rudin is also a neccessity :p.)
A: A good book for metric spaces specifically would be Ó Searcóid's Metric Spaces. However, note that while metric spaces play an important role in real analysis, the study of metric spaces is by no means the same thing as real analysis. 
A good book for real analysis would be Kolmogorov and Fomin's Introductory Real Analysis.
A: A good and concise book would be "Metric and Topologial Spaces" by Sutherland.
Note that metric and topological spaces are highly related.
