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The goal of the present book, resulting from the 7th international conference Algebra, Geometry and Mathematical Physics (AGMP 7) is to extend the understanding of the fundamental role of algebra and geometry, and especially generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics. The event has been very successful in bringing best research in these closely related topics together and in generating important collaborations and insights into the corresponding subjects and applications in physics and engineering. This volume is devoted to the interplay between expanding research directions in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond.