These are the proceedings of the first Woodward conference, which brought together experts from a number of different disciplines to discuss problems involving wave phenomena. Research papers and review papers contain results of interest both to workers and graduate students in electromagnetics, fluid mechanics, atmospheric science, and the theory of anisotropic media. Topics discussed include: - the fast Hartley transform - pseudo-differential operator techniques - inverse scattering problems - nonlinear waves in anisotropic media wave localisation - wave propagation in liquid crystals - solitons - Saffman-Taylor viscous fingering.