**EDIT (Harry):** Since this question in its original form was poorly stated (asked about topology rather than graph theory), but we have a list of Topology books in the answers, I guess you should go ahead and post with regard to that topic, rather than graph theory, which the questioner can ask again in another topic.


EDIT (David): The original question was asking for places to learn topology with an eye towards applying it to computer science (artificial neural networks in particular)



Learning Topology
1. A self study course I can recommend for topology is **Topology** by **JR Munkres** followed by **Algebraic Topology** by **A Hatcher** (freely and legally available online, courtesy of the author!). But that is if you want to be able to really do the math in all its glorious detail. **Basic Topology** by **MA Armstrong** is a shortcut and a very good one at that.
2. The closest I can get to what you are asking for here is [Network Topology](http://en.wikipedia.org/wiki/Network_topology%20%22Network%20Topology%22). Is that what you mean? In that case you should be probably be looking at topological graph theory. Wikipedia also tells me that something called Computational Topology exists, but that is probably not what you are looking for.


Hope that helps!


