Convergence of Riemannian Manifolds

This is a series of lectures on Gromov-Hausdorff convergence. It is not in the least bit comprehensive but should be somewhat accessible to people who have taken just one class in Riemannian geometry.

1. Introduction

2. Critical points of distance functions

3. Almost Maximal Volume

4. Sub-Index of critical points of distance functions

5. Diffeomorphism Stability---A brief survey