Preface
Introduction
1 The concept of a manifold
2 Vector and tensor fields
3 Mappings of tensors induced by mappings of manifolds
4 Lie derivative
5 Exterior algebra
6 Differential calulus of forms
7 Integral calculus of forms
8 Particular cases and applications of Stokes'theorem
9 Poincare lemma and cohomologies
10 Lie groups:basic facts
11 Differential geometry on Lie groups
12 Representations of Lie groups and Lie algebras
13 Actions of Lie groups and Lie algebras on manifolds
14 Hamiltonian mechanics and symplectic manifolds
15 Parallel transport and linear connection on M
16 Field theory and the language of forms
17 Differential geometry on T M and T*M
18 Hamiltonian and Lagrangian equations
19 Linear connection and the frame bundle
20 Connection on a principal G-bundle
21 Gauge theories and connections
22 Spinor fields and the Dirac operator
Appendix A Some relevant algebrai structures
Appendix B Starring
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