Basal nuclei (AKA ganglia) are a group of deep, interconnected grey matter structures located beneath the cerebral cortex (i.e subcortical grey matter). The basal nuclei lie on either side of the internal capsule (are separated and shaped by it). They are involved in:
<aside> đź’ˇ
The slides say “a number of complex subcortical nuclear masses”- a nuclear mass is just a cluster of neuronal cell bodies
</aside>
The basal nuclei include:

In the above diagram, the lefthand side is the anatomical groupings whereas the middle/right is the functional groupings.
So the two functional groups mentioned here are the striatum and the pallidum. The corpus striatum is made up of the putamen and the caudate nucleus, while the pallidum is just made up of the globus pallidus.
The anatomical groupings include the caudate nucleus and the lentiform nucleus, which is made up of the putamen and the globus pallidus.
