Analysis textbook: for those who want to know the Reals

quote from preface: 'One motive for my writing this text is to make available in fairly simple form material that I think of as “calculus done right.” I have tried to write a text which will be helpful to a determined student with an average background. (I seriously doubt that it will be of much use to the chronically lazy or totally unengaged.)' A summer spent working through this material would not be wasted time.