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)