Methods for knowledge discovery in data bases (KDD) have been studied for more than a decade. New methods are required owing to the size and complexity of data collections in administration, business and science. They include procedures for data query and extraction, for data cleaning, data analysis, and methods of knowledge representation. The part of KDD dealing with the analysis of the data has been termed data mining. Common data mining tasks include the induction of association rules, the discovery of functional relationships (classification and regression) and the exploration of groups of similar data objects in clustering. This review provides a discussion of and pointers to efficient algorithms for the common data mining tasks in a mathematical framework. Because of the size and complexity of the data sets, efficient algorithms and often crude approximations play an important role.