1: Vector spaces 2: Multilinear mappings and dual spaces 3: Tensor product spaces 4: Tensors 5: Symmetric and skew-symmetric tensors 6: Exterior (Grassmann) algebra 7: The tangent map of real cartesian spaces 8: Topological spaces 9: Differentiable manifolds 10: Submanifolds 11: Vector fields, 1-forms and other tensor fields 12: Differentiation and integration of differential forms 13: The flow and the Lie derivative of a vector field 14: Integrability conditions for distributions and for pfaffian systems 15: Pseudo-Riemannian manifolds 16: Connection 1-forms 17: Connection on manifolds 18: Mechanics 19: Additional topics in mechanics 20: A spacetime 21: Some physics on Minkowski spacetime 22: Einstein spacetimes 23: Spacetimes near an isolated star 24: Nonempty spacetimes 25: Lie groups 26: Fiber bundles 27: Connections on fiber bundles 28: Gauge theory
Robert H. Wasserman is Professor Emeritus of Mathematics at Michigan State University, USA.
`Review from previous edition Clearly written and self-contained and, in particular, the author has succeeded in combining mathematical rigor with a certain degree of informality in a satisfactory way. As such, this work will certainly be appreciated by a wide audience.' Mathematical Reviews, August 1993