The Cerebellum is a peach-sized structure situated at the base of the brain. It is highly-folded and has been called the brain with the brain - indeed the very name comes from the Latin for "little brain". See this diagram:
The cerebellum controls movement by collecting sensory nerve inputs, such as limb position, balance information and vision, and synthesising them together to control movement by sending nerve transmissions down motor nerve outputs. The learning of physical tasks is done by trial and error and then stored into cerebellar memory. This is the reason that we never forget certain skills such as riding a bike. There is some evidence that mental activities are also co-ordinated in the cerebellum which could explain why cognitive dysfunction is sometimes associated with damage to the cerebellum.
The cerebellum is divided into two hemispheres by the central "vermis". The surface of each hemisphere is made up of grey matter surrounding a large mass of white matter (nerve cells with myelinated axons). The whole structure is connected to the rest of the central nervous system by three very broad tracts of white matter called the cerebellar peduncles. These are the brachium pontis which connects to the pons, the restiform body which connects to the medulla and the brachium conjunctivum which connects to the mesencephalon.
Damage to the cerebellum or the cerebellar peduncles is very common in multiple sclerosis. This is not surprising given the large amount of white matter in these structures.
Some of symptoms associated with damage to the cerebellum or the nervous tracts leading to it are: