I have added a new addition to the Recommended Books for Undergraduate Math, which is one of my most popular posts!
The new book is The Elements of Integration and Lebesgue Measure, an advanced text on the theory of integration. At the high school level, students are exposed to integration, but merely the rules of integration. At university, students learn the Riemann theory of integration (Riemann sums), which is a good theory, but not the best. There are some functions which we would like to integrate, but do not fit nicely into the theory of Riemann Integration.
I am personally reading this book as well, as I didn’t manage to study it in university, but it is a key component for graduate level analysis. Students interested in advanced Probability (see this post on Coursera Probability course) would be needing Lebesgue theory too!