This is the only analysis intro I've found with a good amount of explanation and context to go along with the definitions-theorems-proofs.  Thus, I think it works well as a first analysis text.  It's not an easy book, things move pretty fast, and a lot of times proofs are left as exercises which you wish were spelled out.  Also, it'd be nice if there were answers to the exercises.  But if you're looking for a user-friendly intro to analysis, this is the best one I've come across.