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In 2000, Stephen Hawking stated, “I think the next century will be the century of complexity.” In that spirit, the Santa Fe Institute received two major grants for fundamental research in complexity science from the John Templeton Foundation: 1) “The Principles of Complexity: Understanding the Hidden Sources of Order among the Prodigies of Nature and Culture” (2011-2014), and 2) “Developing a Comprehensive Theory of Complexity” (2015-2017). Here, we propose to produce three in-depth Research Syntheses related to aspects of the previously funded research programs in complexity science suitable for science writers/journalists and the interested public. The three reviews of recent progress in complexity research will be led by early-career scientists who trained at the Santa Fe Institute and will explore the following topics: 1) Autocatalytic Sets as an Example of Complexity in Chemistry and Biology (Wim Hordijk), 2) Deepening Our Understanding of Complexity with Mathematics (Josh Grochow), and 3) Hidden Sources of Order in Complex Human Societies (Stefani Crabtree). Editorial oversight will be provided by Project Leader and SFI Professor and Vice President for Science Jennifer Dunne, with additional editorial input from Geoffrey West, Shannan Distinguished Professor at SFI, both of whom were involved deeply with the prior grant proposals and research activities. SFI’s Communications Manager Jenna Marshall will provide additional editorial input with an eye to accessibility. The SFI Press will aid in promulgating and enhancing the potential reach and impact of the Research Syntheses by publishing them as a single volume in the Compass Series. That series focuses on publishing provoking, exploratory volumes that seek to build complexity literacy for non-scientists: humanities academics, members of industry, and the curious public.