Tao T. Analysis I 4ed 2023

Textbook in PDF format

This is the first book of a two-volume textbook on real analysis. Both the volumes—Analysis I and Analysis II—are intended for honors undergraduates who have already been exposed to calculus. The emphasis is on rigor and foundations. The material starts at the construction of number systems and set theory (Chaps. 1–5), then on to the basics of analysis such as limits, series, continuity, differentiation, and Riemann integration (Chaps. 6–11). There are appendices on mathematical logic and the decimal system.
The fourth edition incorporates a large number of additional corrections reported since the release of the third edition, as well as some additional exercises