1. Riemannian Manifolds
2. Lie Groups and Vector Bundles
3. The Laplace Operator and Harmonic Differential Forms
4. Connections and Curvature
5. Geodesics and Jacobi Fields
6. Symmetric Spaces and Kähler Manifolds
7. Morse Theory and Floer Homology
8. Harmonic Maps between Riemannian Manifolds
9. Harmonic Maps from Riemann Surfaces
10. Variational Problems from Quantum Field Theory
Appendices
A. Linear Elliptic Partial Differential Equations
B. Fundamental Groups and Covering Spaces
Bibliography
Index.