Processing of raw data from modern astronomical instruments is nowadays often carried out using dedicated software, so-called pipelines which are largely run in automated operation. In this paper we describe the data reduction pipeline of the Multi Unit Spectroscopic Explorer (MUSE) integral field spectrograph operated at ESOs Paranal observatory. This spectrograph is a complex machine: it records data of 1152 separate spatial elements on detectors in its 24 integral field units. Efficiently handling such data requires sophisticated software, a high degree of automation and parallelization. We describe the algorithms of all processing steps that operate on calibrations and science data in detail, and explain how the raw science data gets transformed into calibrated datacubes. We finally check the quality of selected procedures and output data products, and demonstrate that the pipeline provides datacubes ready for scientific analysis.
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