This is the second edition of an analysis textbook which starts from the basics (elementary set theory) and covers the usual parts of calculus (continuity, differentiability, integrability, real and complex sequences). However, it also treats two additional topics which may be regarded as an important preparation of functional analysis, viz. metric and normed spaces, on the one hand, and the Lebesgue measure and integral on the real line, on the other. The interested reader may get a more detailed idea of the contents from the review of the first edition [Basic real analysis. Boston, MA: Birkhäuser (2003; Zbl 1035.26001)]. As pointed out there, the main positive characteristic of the book is the wealth of illuminating examples and exercises which make this a valuable textbook on every level of mathematical education.

Reviewer:

Jürgen Appell (Würzburg)