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!
alt text http://ars.els-cdn.com/content/image/1-s2.0-S0925772112000752-gr001.jpg(source)
[Image from "Shortest path problem in rectangular complexes of global nonpositive curvature" (Elsevier link)]