Report 100, Mathematical Techniques in Nuclear Medicine, is a revision of Report No. 73 which was published in 1996. In the intervening years advances in computing power have allowed the development and widespread introduction of powerful reconstruction, correction and analysis techniques. This has been advantageous for Nuclear Medicine as a speciality but provides a challenge for the Nuclear Medicine scientist. Many complex techniques are now readily available at the click of a button. Analysis is often built into automated workflows, where minimal operator interaction is required. Using these without understanding how they work could lead to errors and possible misinterpretation. It is essential that scientific staff working in Nuclear Medicine really understand the theory behind the techniques and how the results are produced. In this way we can produce high quality diagnostic studies which are of value to our clinical colleagues. This report covers the theory behind a wide range of in signal processing techniques used in Nuclear Medicine including; Image processing and display, quantitative measurements, image comparison, deconvolution, parametric images, factor analysis and SPECT reconstruction. Each chapter gives a comprehensive coverage of the underpinning theory as well as practical examples which aid understanding. The report is aimed at Clinical Scientists (from trainees through to senior members of staff) who work in Nuclear Medicine but would also be useful to technologists, radiographers, radiologists and physicians who are interested in understanding more about Nuclear Medicine.