1 Introduction

Last year at the International Congress of Mathematicians (ICM `94) in Zürich, Switzerland one of the four recipients of the Fields Medal was a mathematician from the former Soviet Union--Prof. Efim Zelmanov, now at the University of Wisconsin, USA. He has used techniques from the theory of non-commutative rings to settle a problem in group theory known as the Restricted Burnside Problem. In the following article I attempt to give a flavour of this Problem and the method of its final resolution. The material is largely based on the talk given by Zelmanov given at the ICM `90 held in Kyoto, Japan[13].