Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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A structure-preserving BiJection of a mathematical object into itself. The set of AutoMorphism of an object forms a group with the composition law. When it is possible to build transformation of an object by selecting one of its elements and applying operations to the object, one can separate *inner AutoMorphism""s *outer AutoMorphism""s The latter being transformations for which there is no correspondance with an element of the object. ---- (I am not satisfied with that, it is too much jargon, there should be an example, it does not convey the power of the concept and is just a definition) -- Olivier.