The book aims to propose a theoretical and applicatory framework for extracting formal rules from data. To this end recent approaches in relevant disciplines are examined that bring together two typical goals of conventional Artificial Intelligence and connectionism - respectively, deducing within an axiomatic shell formal rules about a phenomenon and inferring the actual behavior of it from examples - into a challenging inferential framework where we learn from data and understand what we have learned. The goal is to obtain a translation of the subsymbolic structure of the data - stored in the synapses of a neural network - into formal properties described by rules. To capture this journey from synapses to rules and then render it manageable for real world learning tasks, the contributions deal in depth with the following aspects: i. theoretical foundations of learning algorithms and soft computing; ii. intimate relationships between symbolic and subsymbolic reasoning methods; iii. integration of the related hosting architectures in both physiological and artificial brain.