This volume is a collection of papers dealing with harmonic analysis and nonlinear differential equations and stems from a conference on these two areas and their interface held in November 1995 at the University of California, Riverside, in honor of V. L. Shapiro. There are four papers dealing directly with the use of harmonic analysis techniques to solve challenging problems in nonlinear partial differential equations. There are also several survey articles on recent developments in multiple trigonometric series, dyadic harmonic analysis, special functions, analysis on fractals, and shock waves, as well as papers with new results in nonlinear differential equations. These survey articles, along with several of the research articles, cover a wide variety of applications such as turbulence, general relativity and black holes, neural networks, and diffusion and wave propagation in porous media. A number of the papers contain open problems in their respective areas.