This project is a CBMS Regional Conference in the Mathematical Sciences entitled "Non-linear Dispersive Wave Systems". This conference will be held at the University of Central Florida in December, 1990. This field has recently been spurred by developments of practical necessity in many areas of science and engineering, and new ideas have surfaced, giving it yet further impetus. These include fruitful use of algebraic techniques, the extension of Benjamin's stability theory, more reliance on Hamiltonian formulations, the use of computational techniques as an investigative tool, and the new perturbation theories for integrable systems. Professor Benjamin will present a unified mathematical treatment of the classical aspects of the field, as well as new results on hydrodynamic stability and instability.