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Introduction
Basics of Manifolds
Vector Bundles
Vectors and Covectors
Differential Forms
Lie Derivatives
Lie Groups
Frobenius Theorem
Principle Bundles
Connections on Principle Bundles
Curvature of a Connection
Classical Electromagnetism
Yang-Mills Theory
Gauge Theory
The Dirac Monopole
Instantons
What Next?
Discussion of the Exercises.

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