This chapter discusses electroencephalography and the neurophysiology of sleep-wakefulness, where electroencephalography is the technique that has been applied the most to the study of sleep-wakefulness. Electroencephalography involves recording the electrical activity of the brain with the help of surface electrodes placed on the scalp, and the record is called an electroencephalogm (EEG). To record an EEG, the electrodes are placed in the frontal, parietal, temporal and occipital regions according to a precisely defined system. Synchronous activity gets summated to give large waves. Asynchronous activity leads to simultaneous deflections in opposite directions, which cancel each other out. Alpha waves are typically recorded when a person is awake but inattentive. Beta waves are typically recorded when a person is awake and alert. EEG is often recorded for research or investigation of patients continuously for hours, and sometimes overnight. Three states of consciousness are wakefulness, dreamless sleep and dream sleep.