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This volume provides state-of-the-art accounts of exciting recent developments in the rapidly-expanding fields of geometric and cohomological group theory. The research articles and surveys collected here demonstrate connections to such diverse areas as geometric and low-dimensional topology, analysis, homological algebra and logic. Topics include various constructions of Thompson-like groups, Wise's theory of special cube complexes, groups with exotic homological properties, the Farrell-Jones assembly conjectures and new applications of Garside structures. Its mixture of surveys and research makes this book an excellent entry point for young researchers as well as a useful reference work for experts in the field. This is the proceedings of the 100th meeting of the London Mathematical Society series of Durham Symposia.