The gray matter comes in two varieties.In one variety the neurons are layered as in a cake and form a cortex. Examples are the cerebral cortex which covers the cerebral hemispheres, and the cerebellar cortex which envelops the cerebellum. In the second variety of gray matter the neurons are not layered and are organized instead like cashew nuts inside a bowl. They form a nucleus.
Human brain anatomical specimen.
Brain cortex and brain nuclei:
The best example of neurons organized as cortex is the neocortex, often called the cerebral cortex. The intact brain pictured above with all its convolutions (image links to source) is a good illustration. The neocortex is folded in a way that allows a larger surface area to fit within the confines of the human skull. Anatomists call each cortical fold a sulcus, and the smooth area between folds a gyrus. At the base of the specimen pictured above, where it would be situated at the lower rear of one's head, you can see the cerebellar cortex that Damasio discusses. The cerebellum's three lobes are situated adjacent to the brain stem.
When neurons are not layered as in cortex, as we discuss above, they are grouped into a nucleus. The plural of nucleus, as you may know, is nuclei. Understanding the two major ways in which neurons are organized in the brain—as cortex and as nuclei—is most important to making sense of the brain's complex anatomy. In the close-up of the dissected brain to the right, a red oval is drawn around recessed nuclei (image links to source), which will be referred to as subcortical nuclei. Surrounding these subcortical nuclei is the neocortex. We discuss both subcortical nuclei and the neocortex in greater detail later in Part 1 of CorticalBrain.com.
Regarding the image above and many others on this site, Special thanks to John A. Beal from the Department of Cellular Biology and Anatomy, Louisiana State University Health Sciences Center in Shreveport. Professor Beal has made these excellent images accessible through Wikipedia.