The following amicus briefs are a good read introduction to the case:
Brief amici curiae of Bundesverband der Deutschen Industrie e.V., Deutscher Industrie- und Handelskammertag e.V., Ibec clg, Konfederacja Lewiatan, and Mouvement des Enterprises de France filed. (Distributed) http://www.supremecourt.gov/DocketPDF/17/17-2/27520/20180111...
Brief amicus curiae of European Commission on Behalf of the European Union in support of neither party filed. https://www.supremecourt.gov/DocketPDF/17/17-2/23633/2017121...
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These are way to long to read completly, but already a quick browse can be enlightening:
Brief of petitioner United States filed. https://www.supremecourt.gov/DocketPDF/17/17-2/22902/2017120...
Brief of respondent Microsoft Corporation filed. (Distributed) Jan 17 2018 https://www.supremecourt.gov/DocketPDF/17/17-2/27619/2018011...
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HN Readers might also enjoy this one:
Brief amicus curiae of 51 COMPUTER SCIENTISTS filed:
https://www.supremecourt.gov/DocketPDF/17/17-2/28101/2018011...