During the last century the relationship between Fourier analysis and other areas of mathematics has been systematically explored resulting in important advances in geometry, number theory, and analysis. The expository articles in this unified, self-contained volume explore those advances and connections. Specific topics covered included: geometric properties of convex bodies, Radon transforms, geometry of numbers, tilings, irregularities in distributions, and restriction problems for the Fourier transform. Graduate students and researchers in harmonic analysis, convex geometry, and functional analysis will benefit from the book's careful demonstration of how Fourier analysis is used to distill the essence of many mathematical problems in a natural and elegant way.