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This paper presents a critical review of selected topics related to the modelling of cancer
onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical
readership, some of the novel mathematical problems in the field. This review attempts
to capture, from the appropriate literature, the main issues involved in the modelling
of phenomena related to cancer dynamics at all scales which characterise this highly
complex system: from the molecular scale up to that of tissue. The last part of the
paper discusses the challenge of developing a mathematical biological theory of tumour
onset and evolution
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