In this study, I have taken up a multi-class classification problem in order to distinguish four types of brain tumours from each other, in particular, medulloblastoma, malignant glioma, Atypical Teratoid Rhabdoid Tumor (ATRT), and normal cerebellar. The dataset describes a few thousand genes, and their numerical levels of expression in each tumour sample. The aim of the study is to predict a tumour class, given the gene expression data for that tumour. The insights from this study will be particularly useful, especially for tumours like ATRT which are difficult to diagnose. Survival rates of such types of cancer are considerably higher with an early correct diagnosis.