John Coates and Iwasawa Theory

This article is a tribute to the rich and enduring contributions of John Coates in Iwasawa theory. It is beyond the scope of the current article to give a detailed exposition on the entire range of the work of John Coates, as it would involve deep and technical aspects of number theory. We shall therefore focus only on some parts of his work, aiming to keep the exposition as simple and accessible as possible. The work of Kenkichi Iwasawa on the study of class groups in arithmetic deeply influenced John Coates and we shall therefore begin with a review of these ideas.