  In this chapter, we study Information Geometry from a particular
non-parametric or functional point of view. The basic model is a probabilities
subset usually specified by regularity conditions. For example, probability
measures mutually absolutely continuous or probability densities with a given
degree of smoothness. We construct a manifold structure by giving an atlas of
charts as mappings from probabilities to a Banach space. The charts we use are
quite peculiar in that we consider only instances where the transition mappings
are affine. We chose a particular expression of the tangent and cotangent
bundles in this affine setting.
