=GENERAL DESCRIPTION:=
There is no universally accepted definition of an ANN. But perhaps most people in the field would agree that an ANN is a network of many simple processors ("units"), each possibly having a small amount of local memory.
The units are connected by communication channels ("connections") which usually carry numeric (as opposed to symbolic) data, encoded by any of various means. The units operate only on their local data and on the inputs they receive via the connections. The restriction to local operations is often relaxed during training. 
Some ANNs are models of biological neural networks and some are not, but historically, much of the inspiration for the field of ANNs came from the desire to produce artificial systems capable of sophisticated, perhaps "intelligent", computations similar to those that the human brain routinely performs, and thereby possibly to enhance our understanding of the human brain. 
Most ANNs have some sort of "training" rule whereby the weights of
connections are adjusted on the basis of data. In other words, NNs "learn" from examples, as children learn to distinguish dogs from cats based on examples of dogs and cats. If trained carefully, ANNs may exhibit some capability for generalization beyond the training data, that is, to produce approximately correct results for new cases that were not used for training.
NNs normally have great potential for parallelism, since the computations of the components are largely independent of each other. Some people regard massive parallelism and high connectivity to be defining characteristics of ANNs, but such requirements rule out various simple models, such as simple linear regression (a minimal feedforward net with only two units plus bias), which are usefully regarded as special cases of ANNs. (adapted from: http://www.faqs.org/faqs/ai-faq/neural-nets/part1/

One of the simplest forms of artificial neurons (units) is a [[perceptron]].

=Also:=
This is an introductory note on Parallel Distributed Processing, sometimes referred to as (Artificial) Neural Networks or Connectionism. The aim is to describe in general terms the basic elements to such a system. http://www.scism.sbu.ac.uk/inmandw/tutorials/pdp/pdpintro.html

=GENERAL TECHNIQUES:=
Several approaches to neural nets have been developed: A technique used, called ''[[backpropagation]]'', is decribed by Donald R. Tveter on his interesting website: http://www.dontveter.com/bpr/public2.html
Another one is the so-called bayesian network: http://www.niedermayer.ca/papers/bayesian/index.html
Similarly in vein but also nice description: http://www.ai.mit.edu/~murphyk/Bayes/bnintro.html

=Applications:=
Neural nets may be used for pattern recognition, speech recognition, musical [[score following]], etc, etc.

=LINKS:=
Machine Learning and Neural Networks Group - Universities of Florence: http://www.dsi.unifi.it/neural/
Important scientist of neural nets, Stephen Grossberg, has a lists of publications freely available for download: http://cns-web.bu.edu/Profiles/Grossberg/onlinepub.html
http://nl.wikipedia.org/wiki/Neuraal_netwerk (dutch) and http://en.wikipedia.org/wiki/Neural_network (english)