An in depth examination of many of the complex issues associated with planning and optimisation of intensity modulated radiotherapy treatment. It includes: a presentation of current practice, techniques and equipment used by medical physicists and others to deliver radiotherapy treatment; a systems modelling approach in the formulation of a beam model for optimisation, describing the effect of X-rays on human body tissues; a deterministic approach to the inverse problem in radiotherapy, based on weighted iterative least squares is modified to allow an adaptive scaling of the error to improve...