Once in a while, a book comes along that is so wonderfully written, the reader reflexively searches for other books by its author. Understanding Analysis is a prime example of this rare breed (Unfortunately, this is Abbott's only book as far as I know: write more!).<br><br>Undergraduates often begin analysis courses with dread and finish in a state of utter confusion,knowing the definitions of key phrases, and sometimes even being able to supply proofs for some elementary results, but having no intution as to why the main theorems are pertinent.<br><br>But it does not have to be so. 'Understanding Analysis' has the distinction of being so readable, it is sometimes difficult to pry oneself away from its pages and attempt the exercises. On multiple occasions I found myself skimming through the book and reading the various 'special topics' (e.g. Cantor Sets, Integration, Fourier Series) interspersed throughout the book to pique the readers' interest. But most importantly, a reader will come away with an understanding of many theorems in analysis. He or she will begin to develop a vocabulary of results that make sense both mathematically and intuitively, be able to use the results to complete the exercises (which are by no means simple 'plug-and-chug' problems), and be excellently prepared for study at a more advanced level.<br><br>Bottom line: Abbott's book may not be encyclopedaic in content, but it, without a doubt covers a sufficient amount of material to warrant its use for a one-semester course in analysis. My only concern is that after such a fantasticly lucid treatment, students may have difficulty adapting to the vast selection of more advanced, less pedagogical texts available. I sincerely hope Abbott writes a sequel.