[Mini Courses] An introduction to metric geometry

In these series of lectures，I will first give some basic notions and properties of Gromov-Hausdorff convergence concerning metric （length）spaces，and then show some known results related to Gromov-Hausdorff topology. The lectures are planned to be divided into three parts: 

1. The Hausdorff distance, the Gromov-Hausdorff distance, the pointed Gromov-Hausdorff convergence and the equivariant Gromov-Hausdorff convergence;
2. Some known results related to the Gromov-Hausdorff topology of manifolds with Ricci curvature bounded below, including quantitative splitting theorem, volume convergence theorem, "almost volume cones are almost metric cones" and so on;
3. Some applications based on the above theories.