This thesis deals with the problem of newborn seizre detection from the Electroencephalogram (EEG) signals. The ultimate goal is to design an automated seizure detection system to assist the medical personnel in timely seizure detection. Seizure detection is vital as neurological diseases or dysfunctions in newborn infants are often first manifested by seizure and prolonged seizures can result in impaired neuro-development or even fatality. The EEG has proved superior to clinical examination of newborns in early detection and prognostication of brain dysfunctions. However, long-term newborn EEG signals acquisition is considerably more difficult than that of adults and children. This is because, the number of the electrodes attached to the skin is limited by the size of the head, the newborns EEGs vary from day to day, and the newborns are reluctant of being in the recording situation. Also, the movement of the newborn can create artifact in the recording and as a result strongly affect the electrical seizure recognition. Most of the existing methods for neonates are either time or frequency based, and, therefore, do not consider the non-stationarity nature of the EEG signal. Thus, notwithstanding the plethora of existing methods, this thesis applies the discrete wavelet transform (DWT) to account for the non-stationarity of the EEG signals. First, two methods for seizure detection in neonates are proposed. The detection schemes are based on observing the changing behaviour of a number of statistical quantities of the wavelet coefficients (WC) of the EEG signal at different scales. In the first method, the variance and mean of the WC are considered as a feature set to dassify the EEG data into seizure and non-seizure. The test results give an average seizure detection rate (SDR) of 97.4%. In the second method, the number of zero-crossings, and the average distance between adjacent extrema of the WC of certain scales are extracted to form a feature set. The test obtains an average SDR of 95.2%. The proposed feature sets are both simple to implement, have high detection rate and low false alarm rate. Then, in order to reduce the complexity of the proposed schemes, two optimising methods are used to reduce the number of selected features. First, the mutual information feature selection (MIFS) algorithm is applied to select the optimum feature subset. The results show that an optimal subset of 9 features, provides SDR of 94%. Compared to that of the full feature set, it is clear that the optimal feature set can significantly reduce the system complexity. The drawback of the MIFS algorithm is that it ignores the interaction between features. To overcome this drawback, an alternative algorithm, the mutual information evaluation function (MIEF) is then used. The MIEF evaluates a set of candidate features extracted from the WC to select an informative feature subset. This function is based on the measurement of the information gain and takes into consideration the interaction between features. The performance of the proposed features is evaluated and compared to that of the features obtained using the MIFS algorithm. The MIEF algorithm selected the optimal 10 features resulting an average SDR of 96.3%. It is also shown, an average SDR of 93.5% can be obtained with only 4 features when the MIEF algorithm is used. In comparison with results of the first two methods, it is shown that the optimal feature subsets improve the system performance and significantly reduce the system complexity for implementation purpose.