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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