What is the/a main reference book for spaces with curvature bounded from below (CBB spaces/spaces with curvature $\geq \kappa$ in the sense of Alexandrov)? Looking for an up to date reference.



Reference request: metric spaces with curvature bounded from below (CBB) spaces
You may check preliminary version of [our book/3](https://arxiv.org/abs/1903.08539).
Otherwise do "Alexandrov spaces with curvature bounded below" by Burago, Gromov, and Perelman and ["Alexandrov's space with curvatures bounded from below II" by Perelman](https://anton-petrunin.github.io/papers/alexandrov/perelmanASWCBFB2+.pdf).
There are some improvements of the results and proofs, but these two papers are still the main reference source; plus there are surveys by one by Plaut and one by me.


There are also reader friendly introductions one by Shiohama and a chapter in Metric geometry by Burago, Burago and Ivanov.


