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.