This thesis investigates the hypothesis that specific brain states can be identified from spatial patterns on EEG topographic maps. Preliminary work showed that topographic maps of rms EEG data are representative of the actual potential distribution on the scalp and that errors in maps are not significantly affected by the method of interpolation used in their construction. Spatial patterns on the maps were subsequently investigated using spectral analysis. With simulated EEG data, results indicated that maximum entropy (ME) power spectrum estimates (PSEs) are consistently superior to Bartlett and Blackman-Tukey PSEs in terms of error in peak-position and the minimum separation in frequency required to identify two sinusoids. The ME PS analysis of sinusoids in white noise showed that acceptable PSEs could be obtained if the SNR was ≥0 dB. PS analysis of actual EEG data demonstrated that the energy of spatial waves was generally larger in EC (eyes closed) data than in EO (eyes open) data. The mean energy of sagittal waves ( wavelength 18.67 cm) was significantly larger (p <0.01) in EC data than in EO data. The mean value of the entropy was significantly larger (p <0.01) for EO PSEs than for EC PSEs indicating greater uniformity in EO PSEs. Discriminant analysis was used to classify features from EC and EO PSEs. The classification rule correctly identified 91% of PSEs in training data and 96% of PSEs in test data indicating that a stable classification rule was obtained. Analysis of normalized PSEs features (total power in PSE a constant) indicated that EC maps primarily contained waves along the sagittal line while EO maps contained waves in all directions. The discriminant analysis of normalized PSEs correctly classified 86% of PSEs in training data and 92% of PSEs in test data. This work demonstrates that spatial patterns on EEG topographic map can be used to identify specific brain states. It suggests that changes in cerebral organization associated with the EC and EO states are manifested in spatial patterns on EEG topographic maps.