Some Nonlinear Problems in Riemannian Geometry

1 Riemannian Geometry.- 2 Sobolev Spaces.- 3 Background Material.- 4 Complementary Material.- 5 The Yamabe Problem.- 6 Prescribed Scalar Curvature.- 7 Einstein-Kahler Metrics.- 8 Monge-Ampere Equations.- 9 The Ricci Curvature.- 10 Harmonic Maps.- Bibliography*.- Notation.