I am seeking a good introductory reference that could lead to an understanding of
the properties of geodesics in
complete [CAT(0) metric spaces][1].
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!

          
![alt text][2x] [<sup>(source)</sup>][2]
<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<sub>[Image from "Shortest path problem in rectangular complexes of global nonpositive curvature" ([Elsevier link][3])]</sub>


  [1]: http://en.wikipedia.org/wiki/CAT(k)_space
  [2]: http://ars.els-cdn.com/content/image/1-s2.0-S0925772112000752-gr001.jpg
  [3]: http://www.sciencedirect.com/science/article/pii/S0925772112000752
  [2x]: https://i.sstatic.net/yGytL.jpg