Advancements in biomedical signal processing techniques have led Electroencephalography (EEG) signals to be more widely used in the diagnosis of brain diseases and in the field of Brain Computer Interface(BCI). BCI is an interfacing system that uses electrical signals from the brain (eg: EEG) as an input to control other devices such as a computer, wheel chair, robotic arm etc. The aim of this work is to analyse the EEG data to see how humans can control machines using their thoughts.In this thesis the reactivity of EEG rhythms in association with normal, voluntary and imagery of hand movements were studied using EEGLAB, a signal processing toolbox under MATLAB. In awake people, primary sensory or motor cortical areas often display 8-12 Hz EEG activity called ’Mu’ rhythm ,when they are not engaged in processing sensory input or produce motor output. Movement or preparation of movement is typically accompanied by a decrease in this mu rhythm called ’event-related desynchronization’(ERD). Four males, three right handed and one left handed participated in this study. There were two sessions for each subject and three possible types : Imagery, Voluntary and Normal. The EEG data was sampled at 256Hz , band pass filtered between 0.1 Hz and 50 Hz and then epochs of four events : Left button press , Right button press, Right arrow ,Left arrow were extracted followed by baseline removal.After this preprocessing of EEG data, the epoch files were studied by analysing Event Related Potential plots, Independent Component Analysis, Power spectral Analysis and Time-Frequency plots. These analysis have shown that an imagination or a movement of right hand cause a decrease in activity in the hand area of sensory motor cortex in the left side of the brain which shows the desynchronization of Mu rhythm and an imagination or a movement of left hand cause a decrease in activity in the hand area of sensory motor cortex in the right side of the brain. This implies that EEG phenomena may be utilised in a Brain Computer Interface operated simply by motor imagery and the present result can be used for classifier development and BCI use in the field of motor restoration