Neural Networks are kind of declasse these days. Support vector machines and kernel methods are better for more classes of problems then backpropagation. Neural networks and genetic algorithms capture the imagination of people who don't know much about modern machine learning but they are not state of the art.
If you want to learn more about AI and machine learning, I recommend reading Peter Norvig's Artificial Intelligence: A Modern Approach. It's a broad survey of AI and lots of modern technology. It goes over the history and older techniques too, and will give you a more complete grounding in the basics of AI and machine Learning.
Neural networks are pretty easy, though. Especially if you use a genetic algorithm to determine the weights, rather then proper backpropagation.
