On the Classification of Polish Metric Spaces Up to Isometry

Introduction Preliminaries Isometric classification of Polish metric spaces Characterizing the isometry groups of Polish metric spaces Some special cases Isometries of locally compact spaces, I: The pseudo-connected case Isometries of locally compact spaces, II: The general case Isometric classification of locally compact spaces Locally compact ultrametric spaces Some analogies with the model theory of countable structures Open problems.