This Manifesto was produced from the Perspectives Workshop 18262 entitled "10 Years of Web Science" that took place at Schloss Dagstuhl from June 24-28, 2018. At the Workshop, we revisited the origins of Web Science, explored that challenges and opportunities of the Web, and looked ahead to potential futures for both the Web and Web Science. We explain issues that society faces in the Web by the ambivalences that are inherent in the Web. All the enormous benefits that the Web offers - for Information sharing, collective organization and distributed activity, social inclusion and economic growth - will always carry along negative consequences, too, and 30 years after ist creation negative consequnces of the Web are only too apparent. The Web continues to evolve and ist next major step will involve Artificial Intelligence (AI) at large. AI has the potential to amplify positive and negative outcomes, and we explore these possibilities, situating them within the wider debate about the future of regulation and governance for the Web. Finally, we outline the need to extend Web Science as the science that is devoted to the Analysis and Engineering of the Web, to strengthen our role in shaping the future of the Web and present five key directions for capacity building that are necessary to achieve this: (i), supporting interdisciplinarity, (ii), supporting collaboration, (iii), supporting the sustainable Web, (iv), supporting the Intelligent Web and (v), supporting the Inclusive Web. Our writing reflects our background in several disciplines of the social and technical sciences and that these disciplines emphasize topics to various extents. We are acutely aware that our observations occupy a particular point in time and are skewed towards our experience as Western scholars - a limitation that Web Science will need to overcome.