Recently, data mining has been actively researched and widely applied to real world problems. There are many kinds of problems in data mining and frequent itemset mining is a central task for several of these problems.ﾠ In this talk, we approach frequent itemset mining from an algorithm theory perspective.ﾠ In this sense, we focus on two topics.ﾠ One topic is modeling the frequent pattern mining problem.ﾠ Weﾠ introduce the notion of `closed patterns`, and show some interesting properties. Then, we present frequent pattern mining algorithms identifying their bottlenecks and looking at recent implementations.