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A fundamental understanding of droplet dynamics is important for the prediction and optimization of technical systems involving drops and sprays. The Collaborative Research Center (CRC) SFB-TRR 75 was established in January 2010 to focus on the dynamics of basic drop processes, and in particular on processes involving extreme ambient conditions, for example near thermodynamic critical conditions, at very low temperatures, under the influence of strong electric fields, or in situations involving extreme gradients of the boundary conditions. The goal of the CRC was to gain a profound physical understanding of the essential processes, which is the basis for new analytical and numerical descriptions as well as for improved predictive capabilities. This joint initiative involved scientists at the University of Stuttgart, the TU Darmstadt, the TU Berlin, and the German Aerospace Center (DLR) in Lampoldshausen. This first chapter provides a brief overview of the overall structure of this CRC as well as a summary of some selected scientific achievements of the subprojects involved. For further details the reader is referred to the subsequent chapters of this book related to the individual subprojects.