2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101068The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H. Gloeckner and K.-H. Neeb), without any restriction on the dimension or on the characteristic. Two basic features distinguish our approach from the classical real (finite or infinite dimensional) theory, namely the interpretation of tangent- and jet functors as functors of scalar extensions and the introduction of multilinear bundles and multilinear connections which generalize the concept of vector bundles and linear connections.202 + x pages Memoirs of the AMS, to appearDifferential Geometry22E65, 53B05, 53C35, 58A05, 58A20, 53B05, 58A32text