Preface
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Learning paradigms
Error-correction
Competitive
Neural network tasks
Algorithm programming

Neural network learning is in Haykin's book defined as:

Learning is a process by which the free parameters of a neural network are adapted through a process of stimulation by the environment in which the network is embedded. The type of learning is determined by the manner in which the parameter change takes plan.

The changes of synaptical strengths are done in many different ways, depending on the network architecture. These methods in which you update the synaptical strengths are called training algorithms.

In the neural networks science, the training algorithms are one of the fields researched the most. The algorithms today, however, are still too clumsy and slow if the network is large-scaled. Here we will only use networks with some hundred neurons.