Drug resistance – the phenomenon whereby malignant tumours lose their responsiveness to therapeutic agents – is recognized as being the major obstacle to be overcome during the systemic therapy of cancer. In the 1980s and early 1990s an enormous amount of information was developed concerning the molecular mechanisms in the cell that can lead to resistance. In addition, these studies have provided insights into why resistance development is such a common property of cancer cells compared with normal cells.

We have been particularly interested in the processes that underlie the evolution of drug resistance within malignant cell populations and in the mathematical and biological models that have been developed to describe these processes. These models provide a greater intuitive understanding of drug resistance as well as providing insights into the more effective use of our available therapeutic agents.

Mathematical relationships in models may tell us little about specific mechanisms involved in various processes but they are often highly generalizable in terms of their inferences and usually lead to testable hypotheses.

Since we are concerned in this book with quantitative and mathematical models, any review of our own and related studies has to include some of the mathematics involved. The authors are aware of the reaction that is likely to engender in many readers (clinicians and biologists in particular) and the advice that was given to Professor Hawking (‘Each equation in a book decreases its sales by half’) as well as the assessment of the schoolboy diarist and commentator, Nigel Molesworth (‘All maths is friteful and mean 0, unless you are a grate brane’).