Well..I guess you've asked about "neurology". Neurology is one of the biggest sectors in the field of medicine. It is extremely complicated and goes hand in hand with psychiatry as well. A "neuron" is the structural and functional unit of the nervous system. In layman terms, "study of neurons" is neurology but trust me, it's a LOT more than that. Neurologists and neurosurgeons work on people who suffer from nervous system related disorders like Alzheimer's disease, Amylotrophic Lateral Sclerosis, Parkinson's disease, Huntington's chorea, Sciatica and the like.