The purpose of this book is to develop neural nets as a strong theory for both brains and machines. The theory is developed in close correlation with the biology of the neuron and the properties of human reasoning. This approach implies the - Updating the biology of the artificial neuron. The neurosciences have experienced a tremendous development in the last 50 years. One of the main purposes of the present work is to incorporate this knowledge into a strong model of the artificial neuron. Particular attention is devoted to formalizing the complex chemical processes at the synaptic level. This formal language supports both symbolic reasoning and uncertainty processing. - Investigating the properties of expert reasoning. This kind of reasoning is approximate, partial and non-monotonic, and therefore requires special mathematical tools for its formalization, such as fuzzy set theory and fuzzy logic. Three different intelligent systems developed with this technology are presented and discussed.