Alexandrov geometry: foundations

by Stephanie Alexander, Vitali Kapovitch, and Anton Petrunin

Paper version is available at AMS; an older CC-BY version can be downloaded at arXiv. You can also download the source files and the latest version.

Table of contents:

   1. Model plane
   2. Metric spaces
   3. Maps and functions
   4. Ultralimits
   5. Space of spaces
   6. The ghost of Euclid
   7. Dimension theory

   8. Fundamentals of curvature bounded below
   9. Fundamentals of curvature bounded above
   10. Kirszbraun revisited
   11. Warped products
   12. Polyhedral spaces

   13. First order differentiation
   14. Dimension of CAT spaces
   15. Dimension of CBB spaces
   16. Gradient flow

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