With the groundwork laid in the first volume (EMS 15) of theCommutative Harmonic Analysis subseries of theEncyclopaedia, 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 historical development, and ends by bringing thesubject to the level of current research.Table of ContentsI. Multiple Fourier Series and Fourier Integrals. Sh.A.Alimov, R.R.Ashurov, A.K.PulatovII. Methods of the Theory of Singular Integrals. II: Littlewood Paley Theory and its Applications E.M.Dyn'kinIII.Exceptional Sets in Harmonic Analysis S.V.Kislyakov