This volume contains reprints of 30 scientific articles which provide a record of some of the main advances in understanding which have lead us from Edwin Hall's discovery of the effect which bears his name to our current understanding of the quantum Hall efFect. In the process of deciding which articles were to be included in the collection and which were to be left out I became aware of the gaps in my knowledge of the relevant history, both very recent and more distant. The final choices are, I have no doubt, imperfect. I know that they reflect to too large a degree the aspects of, the subject on which I have 'worked myself, so that the collection represents mil perspective on the quantum Hall effect. It is my hope ,however, that the reader will find that these articles taken together have a rather interesting story to tell: a story which reminds us of the unpredictable consequences of scientific enquiry and reflects the impressive achievements of condensed matter physics in this century. The reprints are accompanied by an Introduction which can stand on its own as a brief explanation of the quantum Hall efFect or serve as an primer for the reprinted articles. The point of view taken in the introduction is again my own and is not the only useful one.