Tom Bridges lectured at the summer school on “modulation of water waves“. The lectures gave an introduction to how modulation of relative equilibria can lead to well-known model equations like KdV, KP, Boussinesq, and Gardner equations. The advantage of this approach is that the modulation equations emerge in a “universal form” with the coefficients determined by derivatives of conservation laws evaluated on the basic state. This strategy leads to a range of new applications for such model equations. Background material includes Bridges (2012), Bridges (2013), and Bridges (2014). The slides from Parts 1 and 2 of the lectures can be downloaded here and here. Lecture notes will be forthcoming.