Finding frequent sets of items was first considered critical to mining association rules in the early 1990s. In the subsequent two decades, there have appeared numerous new methods of finding frequent itemsets, which underlines the importance of this problem. The number of algorithms has increased, thus making it more difficult to select proper one for a particular task and/or a particular type of data. This article analyses and compares the twelve most widely used algorithms for mining association rules. The choice of the most efficient of the twelve algorithms is made not only on the basis of available research data, but also based on empirical evidence. In addition, the article gives a detailed description of some approaches and contains an overview and classification of algorithms.