Original: In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields.
Simplified: In number theory, Iwasawa theory is a Galois module theory of ideal class groups, started by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields.