[Math] A good book for metric spaces

Question

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?

Answer 1

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.