Lecture Notes on Symmetric Spaces

1. Definition and Examples (p.2) 2. Transvections and Holonomy (p.7) 3. Killing Fields (p.9) 4. Cartan Involution and Cartan Decomposition (p.11) 5. Locally Symmetric Spaces (p.15) 6. Compact, Noncompact and Euclidean Type; Duality (p.16) 7. The Isometry Group (p.17) 8. Lie Subtriples and Totally Geodesic Subspaces (p.19) 9. Isotropy Representation and Rank (p.19) 10. The Weyl Group (p. 22) References (p.24)