Neural networks for beginners: popular types and applications

Recently there has been a great buzz around the words "neural network" in the field of computer science and it has attracted a great deal of attention from many people. But what is this all about, how do they work, and are these things really beneficial? Essentially, neural networks are composed of layers of computational units called neurons, with connections in different layers. These networks transform data until they can classify it as an output. Each neuron multiplies an initial value by some weight, sums results with other values coming into the same neuron, adjusts the resulting number by the neuron's bias, and then normalizes the output with an activation function.