Abstract: We study immersed hypersurfaces in Rn. Every immersion of M into Rn induces a metric, covariant derivative, volume form, Gauss and mean curvature, ... on M. Since Imm(M,Rn) is a Frechet manifold and thus has a differentiable structure, we can study the infinitesimal variation of these terms as the immersion changes. The obtained formulas are necessary tools to deal with metrics on shape space and surface flows.