Cancer is a global health burden; 1 in 2 people will be diagnosed with some form of cancer during their lifetime. In the Western world, 50% of cancer patients survive for 10 or more years after diagnosis, compared to 24% forty years earlier. Cancer can come in many different forms, but tissues affected by cancer tend to have common features such as abnormal cell growth rates. Cancer biology is incredibly complicated, as illustrated by the difficulties surrounding the diagnosis and treatment of cancer. However, mathematics has the potential to mediate this complexity by abstracting the system using simplifying assumptions into a mathematical framework that can be analysed and/or solved numerically to gain biological insight. This article is an introduction to the mathematical modelling of one of the important early stages of tumour growth – the avascular stage – where there is no blood supply to the tumour.