Nonstandard analysis and differentiable manifolds- Foundations

Abstract. We approach the study of differentiable manifolds modeled on Banach spaces by means of Nonstandard Analysis. We stay inside the cat-egory of classical manifolds and using nonstandard analysis techniques, we present some new nonstandard characterizations for the tangent bundle, differentiable function, differential of a function, directional derivatives, etc. We establish some relations between our definitions and the classical ones