Neurology is the branch of medicine that deals with the study and treatment of nervous system disorders. The nervous system itself is composed of the central nervous nervous system and the peripheral nervous system. 
The central nervous system is the brain and the spinal cord, while the peripheral nervous system is composed of all the other nerves and sensory receptors in the sense organs (such as the eyes, ears, skin etc.).
A doctor who specializes in neurology is called a neurologist, and surgeons who perform surgeries related to neurology are called neurosurgeons.