Neural networks are models which have been developed to simulate the anatomy of the nervous system. The connection between the elements of these networks, the so called artificial neurons, is similar to the connection between the biological neurons. In developing neural networks people are trying to create systems which have the same computational and communication properties as the brain. On the basis of the things we know from neurophysiology the first models for the neural networks are developed. One of these networks was the perceptron, which is one of the most used neural networks. In this thesis we'll study this special neural network. When the input vectors of the perceptron can be linearly separated into two categories, this network can be trained to correctly classify these input vectors. However in most practical cases the linearly separability assumption isn't satisfied. That's why the main part of this study is devoted to the case where the input vectors aren't linearly separable. / Graduation date: 1995