Accumulating evidence from electrocorticogram (ECoG) recordings and imaging challenge traditional views of brain oscillations as spatially stationary periodic sources. Understanding the spatio-temporal dynamics of cortical activity requires novel measurement and analysis methodologies. We recorded broadband local field potential (LFP) across the whole neocortex in freely behaving rats using high-density flexible surface and translaminar arrays using active transistors. 3D tracking and spatio-spectral analysis of recordings over long sessions enabled automatic and accurate brain and behavioral states segmentation. We developed a novel approach for biophysically-inspired detection of the spatio-temporally non-stationary LFP sources allowing decomposition of cortical activity into spatio-temporal waves with diverse temporal scales, direction and speed of propagation as well as topographic origin. Faster waves were embedded into slower ones. Waves of all scales clustered in similar topographic regions. Speed of propagation scaled inversely with the wave time scale. Inter-wave temporal correlational analysis revealed diverse non-stationary spatio-temporal structure within conventionally defined quasi-stationary oscillatory dynamics. Sleep spindles and gamma oscillations were identified as transient and spatially localized oscillatory bursts with single cycles exhibiting complex and often spiraling spatio-temporal structure. Using joint depth and surface recordings we analyzed the intracortical sources underlying cortical waves. Nonstationary spatio-temporal multiscale cortical waves dynamics challenge traditional views of brain oscillations, highlighting the need for a broader understanding of cortical activity patterns in different frequency bands under common biophysically-based unified multiscale dynamics framework.