Basic Analysis: Introduction to Real Analysis

Jirí Lebl

This free online textbook (e-book in webspeak) is a one-semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009 and was later enhanced to teach Math 521 at the University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, and also as the first semester of a more advanced course that also covers topics such as metric spaces.