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First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians.§Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations."§Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations.§Should benefit graduate students and researchers in mathematics and mathematical physics.§