The course starts with introductory lectures on the Navier-Stokes and Euler equations for incompressible fluids in 2 and 3 dimensions, and the surface quasigeostrophic equation (SQG). Long ago, it was hoped that SQG might provide a highly simplified explanation for the formation of weather fronts, but that hope was quickly dispelled. The goal of the course is to prove that for an SQG solution with a weather front as initial data, that weather front survives for a while before breaking up. No specialized background is needed to follow the course.