Published on *www.math.tifr.res.in* (http://www.math.tifr.res.in)

Universitat Heidelberg, Germany

March 11, 2010

Starting from old problems in diophantine geometry we first try to explain how Iwasawa was motivated to develop classical Iwasawa theory. Then we describe the generalisations towards non-commutative Iwasawa theory and we shall make some comments on known results.