Lectures on Gravitational Wave Signatures of Primordial Black Holes

We provide a pedagogical approach to gravitational waves in cosmology with focus on gravitational wave signals related to primordial black holes. These lectures notes contain more details than one is able to present in the two two-hour lectures they are meant to and, as such, they should be thought as a complementary material. The main aim of these lectures is that, by the end, one obtains a certain degree of intuition on gravitational waves in cosmology and understands the basic features of scalar induced gravitational waves. We also highlight must-check properties of induced gravitational waves as well as current issues regarding secondary gravitational waves in cosmology. Throughout the lecture we provide exercises, supplementary information and activities with public codes to be ready to derive your own results.