Pure metric geometry

Here you can download Pure metric geometry by Anton Petrunin. The source files can be downloaded from the project page on GitHub; the final publication is available at Springer. An older (CC BY)-version is available at arXiv:2007.09846.

This text can serve as an introductory part for a variety of courses in metric geometry. We stick to domestic affairs of metric spaces, keeping away from any extra structure. Applications are given only as illustrations.

The only prerequisite is an interest in the subject, but any knowledge of classical geometry, differential geometry, topology, and real analysis will be useful.

Table of contents:

   1. Definitions
   2. Universal spaces
   3. Injective spaces
   4. Space of subsets
   5. Space of spaces
   6. Ultralimits

Please email me comments/corrections/suggestions.