Different facets of interplay between harmonic analysis andapproximation theory are covered in this volume.  The topics included areFourier analysis, function spaces, optimization theory, partial differentialequations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first eventtook place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August2013, at the section “ApproximationTheory and Fourier Analysis”. The secondevent was the conference on Fourier Analysis and Approximation Theory in theCentre de Recerca  Matemàtica (CRM), Barcelona, during 4th-8th November 2013,organized by the editors of this volume. All articles selected to be part ofthis collection were carefully reviewed.