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The aim of the SDANCA-15 Workshop is to summarize the contemporary aspects and to formulate in a concise form the open problems in the study of nuclear structure and dynamics in the presence of different kinds of shape deformations. The idea is to combine up-to-date theoretical and experimental knowledge on the subject and to outline a common study direction focused on the search for and description of new shape phenomena and their effect on nuclear structure and stability in different mass regions. A major practical aim of the Workshop is to connect scientists with mutually complementary expertise and to inspire possible new collaborations on the subject of complex nuclear deformations.