Monodromy is a fundamental yet elusive concept in algebraic geometry: while its definition is simple, computing it can be surprisingly difficult. This challenge has fascinated mathematicians for centuries, as monodromy appears naturally in various problems of algebraic geometry and has plenty of applications. After introducing some general techniques to approach monodromy computations, we illustrate a panorama of results and perspectives. Time permitting, we are going to see key examples, ranging from easy to hard, on Abel’s theorem and the impossibility of solving degree five equations by radicals, as well as on Fano problems, with a focus on the 27 lines on a cubic surface.
