The purpose of this summer school is to offer graduate students and young researchers a number of crash courses related to the analysis of a certain class of PDEs arising in fluid mechanics. We invited a number of world-renowned experts in the field, who each will give a 4 lecture series over the course of one week, talking about state-of-the-art tools and highlighting the main ideas used in recent developments in fundamental PDEs of fluid mechanics. In particular, ideas used in analyzing models such as incompressible Euler, Navier-Stokes, and various active scalars will be overviewed. In addition, the summer school will include a mini-symposium, where participants will be encouraged to speak about their own research.