TITLE: Source for: Geodesics in CAT(0) spaces
QUESTION [9 upvotes]: I am seeking a good introductory reference that could lead to an understanding of
the properties of geodesics in
complete CAT(0) metric spaces.
I am especially interested in learning the differences between geodesics in these spaces
and those in an $n$-dimensional Euclidean space with its usual Euclidean metric,
which is of course CAT(0).
I am ultimately interested in simplicial, cubical, and polyhedral complexes,
but I am willing to start anywhere.  Thanks for educating me!
          
 (source)
          
[Image from "Shortest path problem in rectangular complexes of global nonpositive curvature" (Elsevier link)]

REPLY [2 votes]: A more recent reference for geodesics is the following preprint: 
Koyo Hayashi. A polynomial time algorithm to compute geodesics in CAT(0) cubical complexes. Oct 2017, arXiv:1710.09932.
Even though the title says "cubical complexes", from the abstract:

Our algorithm is applicable to any CAT(0) space in which geodesics between two close points can be computed, not limited to CAT(0) cubical complexes.