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With the groundwork laid in the first volume (EMS 15) of theCommutative Harmonic Analysis subseries of the Encyclopaedia, the present volume takes up four advancedtopics in the subject: Littlewood-Paley theory for singularintegrals, exceptional sets, multiple Fourier series andmultiple Fourier integrals. The authors assume that thereader is familiar with the fundamentals of harmonicanalysis and with basic functional analysis. The expositionstarts with the basics for each topic, also taking accountof the historicaldevelopment, and ends by bringing thesubject to the level of current research.