A human brain is the most important organ which controls the functioning of the body including heartbeat and respiration. It is an extremely complex system. Electroencephalography (EEG) is the recording of electrical activity along the scalp produced by the firing of neurons within the brain. In clinical context EEG refers to the recording of the brain's spontaneous electrical activity over a short period of time, say 20-40 minutes, as recorded from multiple electrodes placed on the scalp. The main application of EEG is in the case of epilepsy, as epileptic activity can create clear abnormalities on a standard EEG study. A secondary clinical use of EEG is in coma, Alzheimer's disease, encephalopathies, and brain death. However in the recent years EEG is also being used to design the brain of a robot. Mathematical concepts specially methods for numerical solution of partial differential equations with boundary conditions, inverse problem methods and wavelet analysis have found prominent position in the study of EEG. The present paper is devoted to this theme and will highlight the role of wavelet.methods. It will also include the results obtained in our research project.