We give an introduction to Riemannian geometry, beginning with the notion of a manifold. We'll study geodesics, Jacobi fields and the Morse index theorem, the curvature tensor and comparison theorems, connections between curvature and topology and time-permitting some selected topics in geometric analysis.
do Carmo Riemannian geometry ; Milnor Morse theory
real analysis, basic point set topology
Schedule of Sections: