The widely used electroencephalogram-based indices for depth-of-anesthesia monitoring assume that the same index value defines the same level of unconsciousness for all anesthetics. In contrast, we show that different anesthetics act at different molecular targets and neural circuits to produce distinct brain states that are readily visible in the electroencephalogram. We present a two-part review to educate anesthesiologists on use of the unprocessed electroencephalogram and its spectrogram to track the brain states of patients receiving anesthesia care. Here in part I, we review the biophysics of the electroencephalogram and the neurophysiology of the electroencephalogram signatures of three intravenous anesthetics: propofol, dexmedetomidine, and ketamine, and four inhaled anesthetics: sevoflurane, isoflurane, desflurane, and nitrous oxide. Later in part II, we discuss patient management using these electroencephalogram signatures. Use of these electroencephalogram signatures suggests a neurophysiologically based paradigm for brain state monitoring of patients receiving anesthesia care.