Cerebral Cortex - Part I The cerebral cortex is the outer grey matter layer covering the entire surface of the two cerebral hemispheres. It is approximately 2 to 4 millimetres thick and is composed primarily of neuronal cell bodies, dendrites, synapses, and supporting glial cells. The cortex lies immediately deep to the pia mater and follows the contours of the cerebral hemispheres. The surface of the cerebral cortex is folded into elevations called gyri and grooves called sulci. This folding in