Memoirs of the American Mathematical Society 2008; 202 pp; softcover Volume: 192 ISBN10: 0821840916 ISBN13: 9780821840917 List Price: US$77 Individual Members: US$46.20 Institutional Members: US$61.60 Order Code: MEMO/192/900
 The 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, without any restriction on the dimension or on the characteristic. Two basic features distinguish the author's 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. Table of Contents  Introduction
 Basic notions
 Interpretation of tangent objects via scalar extensions
 Second order differential geometry
 Third and higher order differential geometry
 Lie theory
 Diffeomorphism groups and the exponential jet
 Appendix L. Limitations
 Appendix G. Generalizations
 Appendix: Multilinear geometry
 References
