This thesis deals with analysis and processing of the Sleep Electroencephalogram (EEG) signals. The scope of this thesis can be split into several areas. The first area is application of the Independent Component Analysis (ICA) method for EEG signal analysis. A model of EEG signal formation is proposed and conditions under which this model is valid are examined. It is shown that ICA can be used to remove non-deterministic artifacts contained in the EEG signals. The second area of interest is analysis of stationarity of the Sleep EEG signal. Methods to identify stationary signal segments and to analyze statistical properties of these stationary segments are presented. The third area of interest focuses on spectral analysis of the Sleep EEG s...