I. Electromagnetism. 1. Maxwell's Equations. 2. Manifolds. 3. Vector Fields. 4. Differential Forms. 5. Rewriting Maxwell's Equations. 6. DeRham Theory in Electromagnetism -- II. Gauge Fields. 1. Symmetry. 2. Bundles and Connections. 3. Curvature and the Yang-Mills Equation. 4. Chern-Simons Theory. 5. Link Invariants from Gauge Theory -- III. Gravity. 1. Semi-Riemannian Geometry. 2. Einstein's Equation. 3. Lagrangians for General Relativity. 4. The ADM Formalism. 5. The New Variables.