ANALYSIS ON MANIFOLDS AND FIBRE BUNDLES is to acquaint students with the basic concepts, so that they can go throught the books on Riemannian Geometry, Lorentzian Geometry, Cartan Geometry etc. Covariant derivative on vector bundles and connection from on principal bundles are the two heroes of Analysis on Fibre Bundles. This will be used in books on Geometry to define curvatures of the respective bundles. Of course curvature (Gauge Field) is the hero of modern Physics because everything is a manifestation of curvature of spacetime. The book is suitable as a text for Mathematics and Physics students at the post-graduate level.

• Classical n-surfaces are discussed • A complete picture of connection form on a principal bundle is given • Deals with classical n-surfaces and modern n-manifolds • Covariant derivative is discussed • Tangent vectors and differential of a map are defined.

Preface / Partition of Unity / Implicit Mapping Theorem / Covariant Derivative / Three Fundamental Theorems / Fibre Bundles / Appendix / References / Symbols / Index.

Under & Postgraduate Students, Teachers and Researchers