Inductive databases (IDBs) have been proposed to afford the problem of knowledge discovery from huge databases. With an IDB the user/analyst performs a set of very different operations on data using a query language, powerful enough to perform all the required elaborations, such as data preprocessing, pattern discovery and pattern postprocessing. We present a synthetic view on important concepts that have been studied within the cInQ European project when considering the pattern domain of itemsets. Mining itemsets has been proved useful not only for association rule mining but also feature construction, classification, clustering, etc. We introduce the concepts of pattern domain, evaluation functions, primitive constraints, inductive queries and solvers for itemsets. We focus on simple high-level definitions that enable to forget about technical details that the interested reader will find, among others, in cInQ publications.