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The Handbook of LHC Higgs cross sections: 4. Deciphering the nature of the Higgs sector is finally finished. This 868 page report summarizes the results of the activities of the LHC Higgs Cross Section Working Group in the period 2014-2016. The report has many contributions from HiggsTools members including ESRs Agnieszka Ilnicka, Stephen Jones, Davide Napoletano and Zahari Kassabov. Fabio Maltoni, Chiara Mariotti and Markus Schumacher are part of the editorial team. Its a great read and is available at https://arxiv.org/abs/1610.07922.