When I was book review editor of The Mathematical Gazette hardly a week went past without the arrival of yet another new book called An introduction to analysis. I began to think that authors and publishers were mad to invest their time and efforts in such ventures. So why on earth am I joining the ranks of those eccentrics?

Pressure upon me to write Yet another introduction to analysis came from ‘above’ and from ‘below’. Following the success of my book on metric spaces (a down-to-earth but fairly rigorous approach to analysis for students in a second year at university or polytechnic) I had letters asking me to recommend a similar first-year text, and I did not know of any. But that in itself was not enough to spur me to enter this highly over-supplied market.

Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be well motivated, relevant and practical. In Britain we now have the GCSE examination which has exactly those aims. My own daughter was one of the first students to take that examination and by the time students like her reach higher education not only will they have greater expectations of the subject but they will also have been less exposed to formal mathematics than their predecessors: surely our first-year university and college courses will have to take account of this?