Currently, more concern towards preterm infants is done due to their earlier birth and premature conditions which make them need more care. The preterm infants are approximately 10% of all total international births. EEG becomes one of the important tests to monitor newborns regardless their stage of birth. This examination grabbed the attention of neuroscientists since 1950s. Most of preterm neonates suffer from brain injuries and abnormal activities. Series EEG recordings are necessary directly after the birth to help in improving preterm infants' health and to increase their probability of surviving. The objective of this work is to familiarize with biomedical signal features, to understand the characteristics of EEG, to introduce preterm infants, to understand their brain problems though EEG monitoring, and to know the pattern and stages of sleep.