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Lecture 01 - Introduction/Logic of Propositions and Predicates

Lecture 02 - Axioms of Set Theory

Lecture 03 - Classification of Sets

Lecture 04 - Topological Spaces - Construction and Purpose

Lecture 05 - Topological Spaces - Some Heavily Used Invariants

Lecture 06 - Topological Manifolds and Manifold Bundles

Lecture 07 - Differential Structures: Definition and Classification

Lecture 08 - Tensor Space Theory I: Over a Field

Lecture 09 - Differential Structures: the Pivotal Concept of Tangent Vector Spaces

Lecture 10 - Construction of the Tangent Bundle

Lecture 11 - Tensor Space Theory II: Over a Ring

Lecture 12 - Grassmann Algebra and deRham Cohomology

Lecture 13 - Lie Groups and Their Lie Algebras

Lecture 14 - Classification of Lie Algebras and Dynkin Diagrams

Lecture 15 - The Lie Group SL(2,C) and its Lie Algebra sl(2,C)

Lecture 16 - Dynkin Diagrams from Lie Algebras, and Vice Versa

Lecture 17 - Representation Theory of Lie Groups and Lie Algebras

Lecture 18 - Reconstruction of a Lie Group from its Algebra

Lecture 19 - Principal Fibre Bundles

Lecture 20 - Associated Fibre Bundles

Lecture 21 - Connections and Connection 1-Forms

Lecture 22 - Local Representations of a Connection on the Base Manifold: Yang-Mills Fields

Lecture 23 - Parallel Transport

Lecture 24 - Curvature and Torsion on Principal Bundles

Lecture 25 - Covariant Derivatives

Lecture 26 - Application: Quantum Mechanics on Curved Spaces

Lecture 27 - Application: Spin Structures

Lecture 28 - Application: Kinematical and Dynamical Symmetries

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