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Radiomics and deep learning have shown high popularity in automatic glioma grading. Radiomics can extract hand-crafted features that quantitatively describe the expert knowledge of glioma grades, and deep learning is powerful in extracting a large number of high-throughput features that facilitate the final classification. However, the performance of existing methods can still be improved as their complementary strengths have not been sufficiently investigated and integrated. Furthermore, lesion maps are usually needed for the final prediction at the testing phase, which is very troublesome. In this paper, we propose an expert knowledge-guided geometric representation learning (ENROL) framework . Geometric manifolds of hand-crafted features and learned features are constructed to mine the implicit relationship between deep learning and radiomics, and therefore to dig mutual consent and essential representation for the glioma grades. With a specially designed manifold discrepancy measurement, the grading model can exploit the input image data and expert knowledge more effectively in the training phase and get rid of the requirement of lesion segmentation maps at the testing phase. The proposed framework is flexible regarding deep learning architectures to be utilized. Three different architectures have been evaluated and five models have been compared, which show that our framework can always generate promising results.