In this work, we develop a computational tool to predict the patient-specific evolution of a highly malignant brain tumour, the glioblastoma multiforme (GBM), and its response to therapy. A diffuse-interface mathematical model based on mixture theory is fed by clinical neuroimaging data that provide the anatomical and microstructural characteristics of the patient brain. The model is numerically solved using the finite element method, on the basis of suitable numerical techniques to deal with the resulting Cahn-Hilliard type equation with degenerate mobility and single-well potential.The results of simulations performed on the real geometry of a patient brain quantitatively show how the tumour expansion dependens on the local tissue structure. We also report the results of a sensitivity analysis concerning the effects of the different therapeutic strategies employed in the clinical Stupp protocol. The simulated results are in qualitative agreement with the observed evolution of GBM during growth, recurrence and response to treatment. Taken as a proof-of-concept, these results open the way to a novel personalized approach of mathematical tools in clinical oncology. K E Y W O R D S diffuse-interface model, finite element, glioblastoma multiforme, mixture theory, personalized medicine M S C ( 2 0 1 0 ) 35K57, 35K65, 35Q92, 65M60, 92C50