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These notes are based on the ten lectures that the author held in Septemberof 2013 at the University of Seville. The purpose of the course was tointroduce basic concepts about the Ahlfors-Beurling operator and explain a fewof the recent (already published or known) results and techniques focusedaround it.

Analysis of the Ahlfors-Beurling operator (lecture notes for the summer school at the University of Seville, 2013)