With the current focus on deep learning, neural networks are all the rage again. (Neural networks have been described for more than 60 years, but it wasn't until the the power of modern computing systems became available that they have been successfully applied to tasks like image recognition.) Neural networks are the fundamental predictive engine in deep learning systems, but it can be difficult to understand exactly what they do. To help with that, Brandon Rohrer has created this from-the-basics guide to how neural networks work:
In R, you can train a simple neural network with just a single hidden layer with the nnet package, which comes pre-installed with every R distribution. It's a great place to start if you're new to neural networks, but the deep learning applications call for more complex neural networks. R has several packages to check out here, including MXNet, darch, deepnet, and h2o: see this post for a comparison. The tensorflow package can also be used to implement various kinds of neural networks.
Data Science and Robots Blog: How neural networks work