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Turbulence is ubiquitous in science, technology and daily life and yet, despite years of research, our understanding of its fundamental nature is still tentative and incomplete. More generally, the tools required for a deep understanding of strongly interacting many-body systems remain underdeveloped. Inspired by a research programme held at the Newton Institute in Cambridge, this book contains reviews by leading experts that summarize our current understanding of the nature of turbulence from theoretical, experimental, observational and computational points of view. The articles cover a wide range of topics, including the scaling and organized motion in wall turbulence, small scale structure, dynamics and statistics of homogeneous turbulence, turbulent transport and mixing, and effects of rotation, stratification and magnetohydrodynamics, as well as superfluidity. The book will be useful to researchers and graduate students interested in the fundamental nature of turbulence at high Reynolds numbers.