Having taken Pugh's honors analysis course, in which he used this book, I can strongly reccommend it to any student interested in the subject of analysis, especially students seeking to learn more than the average introductory real analysis book contains. Pugh's book contains advanced theorems and topics not often found in undergraduate level texts. Additionally, the problems are well thought out and tend to be of a high level of difficulty.

This is one of the best books on introductory real analysis that I have looked at. Before I found this book, I have been reading another work on real analysis which was also very good, but was far less comprehensive. Not only does this book present a precise exposition of concepts and theorems, it also gives illustrations to better explain the ideas and plenty of excercises at the end of each chapter. For example, the author does not only say what a "covering" means, but he gives an illustration of it. The style of exposition is fine and relaxed, but the rigor of presentation of theorems and proofs is not in the least compromised. I would think that this book will be of enormous help to anyone trying to make a transition from concrete to more abstract mathematical reasoning.