The current thesis is devoted to knowledge extraction from trained artificial neural networks (ANN). Artificial neural networks frequently show excellent results in classification problems, but in many cases, they are unusable due to a lack of understanding of how classification decision is made. Black-box nature severely limits ANN applicability, especially in mission-critical domains like medicine, nuclear energy, finance, and others. Extracted knowledge allow domain expert to validate model classification decision. For validation, an expert requires comprehensible rules with a simple structure. Also extracted knowledge can be embedded in other systems, i.e., databases. In the latter case, rules classification precision is of higher importance than rules set size and comprehensibility, which is needed for a human expert to understand classification decision. The thesis presents a developed methodology for knowledge extraction from trained ANN. The methodology provides an overview of knowledge representation schemas. Highlights pros and cons, and concentrates on the knowledge extraction in the form of a classification decision tree, from ANN, If-Then rules extraction from a piece-wise linear classifier and elliptical rules extraction from a radial basis function ANN (RBFNN). The last two approaches are optimization-based. Decision tree and elliptical rule extraction approaches are applicable to any classifier. The thesis presents a developed, pruning approach that improves ANN generalization. Comparison of neurons versus weights pruning effect is provided as well. The methodology provides experimentally validated recommendations for extracting precise or simple, understandable rules.