This text is the result of two complementary experiences which I had in 1987 and 1988. The first was the opportunity, which I owe to Claude Godrèche, of delivering, in a pleasant seaside resort in Brittany, a series of lectures on the theory of neural networks. Claude encouraged me to write the proceedings in the form of a pedagogical book, a text which could be useful to the many people who are interested in the field. The second was a one-year sabbatical which I spent at the Hebrew University of Jerusalem on a research program on spin glasses and neural networks. The program was initiated by the Institute for Advanced Studies and organized by a team of distinguished physicists and biologists, namely Moshe Abeles, Hanoch Gutfreund, Haim Sompolinsky and Daniel Amit. Throughout the year, the Institute welcomed a number of researchers who shed different lights on a multi-faceted subject. The result is this introduction to the modeling of neural networks.

First of all, it is an introduction. Indeed the field evolves so fast that it is already impossible to have its various aspects encompassed within a single account.

Also it is an introduction, that is a peculiar perspective which rests on the fundamental hypothesis that the information processed by the nervous systems is encoded in the individual neuronal activities. This is the most widely admitted point of view. However, other assumptions have been suggested.