摘要：One of the most challenging topic in number theory is to understand the mysterious relationship between the special values of complex L-functions and arithmetic objects like class groups, Selmer groups etc. At present, Iwasawa theory provides the only known general method for studying these problems. In this talk, I will give an overview of Iwasawa theory and describe the motivation behind the reason of its study. This talk will be expository (as possible). In the event if time permits, I will also briefly mention some of my work concerning about the study of the Selmer groups over an infinite (possibly noncommutative) extension of a number field and describe how they correlate with the theme.