We used a new methodological approach to the evaluation of EEG synchronization based on correlation between amplitude modulation processes (EEG envelopes). We revealed: left-hemispheric dominance and dominance of frontal over occipital regions characteristic of all sleep stages; differences in synchronization in frequency bands and their patterns characteristic of a specific sleep stage; stage-dependent differences in inter-hemispheric synchrony and patterns of their changes from the frontal to occipital regions; and stage-dependent topographical distributions of high synchronization foci with respect to frequency domains. Analysis of amplitude topography also revealed left-hemispheric dominance and many significant differences in activity distribution patterns over parasagittal chains of electrodes (meridians) depending on sleep stages and frequency domains. The combination of EEG synchrony estimates with the amplitude spectral estimates made it possible to perform a reliable discriminant recognition of five sleep stages with errors in the range of 3-20%.