数学分析基础，比国内的同类教材深一点。 This book is intended to serve as a text for the course in analysis that is usually taken by advanced undergraduates or by first-year students who study mathe- matics. The present edition covers essentially the same topics as the second one, with some additions, a few minor omissions, and considerable rearrangement. I hope that these changes will make the material more accessible amd more attrac- tive to the students who take such a course. Experience has convinced me that it is pedagogically unsound ( though logically correct) to start off with the construction of the real numbers from the rational ones. At the beginning, most students simply fail to appreciate the need for doing this. Accordingly, the real number system is introduced as an ordered field with the least-upper-bound property, and a few interesting applications of this property are quickly made. However, Dedekind's construction is not omit- ted. It is now in an Appendix to Chapter 1, where it may be studied and enjoyed whenever the time seems ripe.