Gliomas are the most frequent primary brain tumors. Their malignancies are graded from 1 to 4. Malignant gliomas are astrocytoma grade 3 and glioblastoma grade 4. An IR spectroscopic approach is presented to diagnose brain tissue at the molecular level probing chemical and structural properties without external markers. IR spectroscopic maps were recorded in transmission mode by sequential acquisition of IR spectra. Training spectra of various tissue types are selected from IR spectroscopic maps in accordance with histological assessment of hematoxylin and eosin stained parallel tissue sections. A decrease of the lipid-to-protein ratio in IR spectra is correlated with the malignancy of gliomas. This chemical property is described by the band intensity ratio 2850 to 1655 cm^-1. Two additional molecular descriptors are identified at 1545 cm^-1/1655 cm^-1 and (1231 + 1450) cm^-1/1655 cm^-1, which are associated with hemoglobin and collagen, respectively. This metric is used to train a classification model based on linear discriminant analysis. The model is applied to classify normal brain tissue, astrocytoma grade 2, astrocytoma grade 3, glioblastoma, hemorrhage, and leptomeninges in IR spectroscopic maps of cryosections from two glioma patients. As independent test samples, single IR spectra from cryosections of 51 patients are subjected to the classification model. Normal brain tissue is assigned with 100% accuracy; malignant gliomas are assigned with 93% accuracy. The high success rate demonstrates that IR spectroscopy can complement established methods such as histopathology or immunohistochemistry to characterize dried cryosections.