The next lecture in this series is here.
We introduce modular forms, and give several examples of how they were used to solve problems in apparently unrelated areas of mathematics.
I will not be following any particular book, but if anyone wants a suggestion for a book I recommend A course on arithmetic by J.-P. Serre (Chapter VII) and Modular functions and Dirichlet series in number theory by T. Apostol.
Typo: at 7:05 the definition of q at the bottom is missing a minus sign in the exponent.
This video is part of a lecture course by Richard Borcherds from 2021.