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The Jordan-Lie functor.- I: Symmetric spaces and the Lie-functor.- II: Prehomogeneous symmetric spaces and Jordan algebras.- III: The Jordan-Lie functor.- IV: The classical spaces.- V: Non-degenerate spaces.- Conformal group and global theory.- VI: Integration of Jordan structures.- VII: The conformal Lie algebra.- VIII: Conformal group and conformal completion.- IX: Liouville theorem and fundamental theorem.- X: Algebraic structures of symmetric spaces with twist.- XI: Spaces of the first and of the second kind.- XII: Tables.- XIII: Further topics.Includes supplementary material: sn.pub/extras