The contribution to this volume comes from non-linear functional analysis and is motivated by a traditional part of physics. More precisely, the motivation arises from elasticity theory : Given a body, thought of as a smooth compact manifold M', possibly with boundary, moving and deforming in IRn,the latter equipped with a fixed scalar product. The deformations shall be such that the diffeomorphism type does not change. Hence M' is the image under a smooth embedding of a smooth compact manifold M, possibly with boundary ∂M. Therefore the collection E(M,IRn) of all smooth embeddings of M into IRn is the collection of all the configuration under considerations. It is a Fréchet manifold if endowed with the C∞-topology.
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