Date | Topic | Lecture notes | Exercises |

10. February 2015 | Introduction. Manifolds. Coordinates. Maps. | lecture01.pdf | ex01.pdf |

17. February 2015 | Fiber bundles. Vector bundles. Sections. | lecture02.pdf | ex02.pdf |

3. March 2015 | Tangent bundle. Vector fields. | lecture03.pdf | ex03.pdf |

10. March 2015 | Cotangent bundle. Tensor bundles. | lecture04.pdf | ex04.pdf |

24. March 2015 | Differential forms. Exterior derivative. | lecture05.pdf | ex05.pdf |

31. March 2015 | Pushforward. Pullback. Coordinate transformations. | lecture06.pdf | ex06.pdf |

7. April 2015 | Integration. Line integrals. Integrals over chain complexes. | lecture07.pdf | ex07.pdf |

14. April 2015 | Jets. Jet manifolds. Jet bundles. | lecture08.pdf | ex08.pdf |

21. April 2015 | Variational bicomplex. Lagrangians. | lecture09.pdf | ex09.pdf |

28. April 2015 | Action principle. Euler-Lagrange equations. | lecture10.pdf | ex10.pdf |

5. May 2015 | Lie groups. Lie group actions. | lecture11.pdf | ex11.pdf |

12. May 2015 | Diffeomorphism groups. Lie derivative. Flow. | lecture12.pdf | ex12.pdf |

12. May 2015 | Noether theorem. | lecture13.pdf | ex13.pdf |

19. May 2015 | Principal fiber bundles. Associated fiber bundles. | lecture14.pdf | ex14.pdf |

26. May 2015 | Connections on fiber bundles. Connection forms. Covariant derivative. | lecture15.pdf | ex15.pdf |

26. May 2015 | Gauge theories. Gauge transformations. | lecture16.pdf | ex16.pdf |