In this thesis, a detailed study shows that closed itemsets and minimal generators play a key role for concisely representing both frequent itemsets and association rules. These itemsets structure the search space into equivalence classes such that each class gathers the itemsets appearing in the same subset aka objects or transactions of the given data. In this respect, we proposed lossless reductions of the minimal generator set thanks to a new substitution-based process. Our theoretical results are extended to the association rule framework in order to reduce as much as possible the number of retained rules without information loss. We then give a thorough formal study of the related inference mechanism allowing to derive all redundant association rules, starting from the retained ones. We also lead a thorough exploration of the disjunctive search space, where itemsets are characterized by their respective disjunctive supports, instead of the conjunctive ones. This exploration is motivated by the fact that, in some applications, such information brings richer knowledge to the end-users. To obtain a redundancy free representation of the disjunctive search space, an interesting solution consists in selecting a unique element to represent itemsets covering the same set of data. Two itemsets are equivalent if their respective items cover the same set of data. In this regard, we introduced a new operator dedicated to this task. In each induced equivalence class, minimal elements are called essential itemsets, while the largest one is called disjunctive closed itemset. The introduced operator is then at the roots of new concise representations of frequent itemsets. We also exploit the disjunctive search space to derive generalized association rules. These latter rules generalize classic ones to also offer disjunction and negation connectors between items, in addition to the conjunctive one.