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This monograph is devoted to theoretical and experimental study of partial reducts and partial decision rules on the basis of the study of partial covers. The use of partial (approximate) reducts and decision rules instead of exact ones allows us to obtain more compact description of knowledge contained in decision tables, and to design more precise classifiers. Algorithms for construction of partial reducts and partial decision rules, bounds on minimal complexity of partial reducts and decision rules, and algorithms for construction of the set of all partial reducts and the set of all irreducible partial decision rules are considered. The book includes a discussion on the results of numerous experiments with randomly generated and real-life decision tables. These results show that partial reducts and decision rules can be used in data mining and knowledge discovery both for knowledge representation and for prediction.