With advances in high-density epicortical electrophysiological recordings (i.e., ECoGs), it became possible to investigate precise spatio-temporal evolution of neural dynamics behind various cognitive functions. This improved resolution allowed for investigation of until now largely disregarded spatial features of neuronal oscillations and challenged the conventional view of global zero-lag synchrony as a basis of neuronal communication. More specifically, it revealed structured phase-offsets in superficial cortical singals corresponding to wave-like dynamics. Further investigation of single-cycle behaviour of these 'waves' and their spatio-temporal structure is crucial to advancing of our understanding of neuronal mechanisms underlying various cortical functions. In addition, combining superficial recordings with laminar probes can help uncover corresponding local neuronal sources and circuit dynamics. Using novel flexible surface active transistor arrays and depth probes we recorded cortex-wide local field potential (LFP) across multiple physiological and behavioural states in freely-behaving rats. We first decomposed the signal into non-stationary non-sinusoidal narrow-band components using a data-driven approach. We then devised a new biophysically-inspired algorithm to track and characterize LFP sources as spatio-temporal waves with diverse temporal scales, direction and speed of propagation, topographic origin amongst other features. Using this multi-dimensional characterization, we mapped these wave events to different brain states revealing them as a useful tool in brain state analysis. Inter-wave temporal correlational analysis revealed heterogeneous non-stationary spatio-temporal structure of conventionally quasi-stationary oscillatory dynamics. Sleep spindles and gamma oscillations were identified as transient and spatially localized oscillatory bursts with single cycles exhibiting complex and spiraling phase portraits, whereas slow timescale waves exhibited translational displacement along the antero-posterior axis in keeping with previous findings. Using joint depth and surface recordings we analyzed intra-cortical sources underlying these cortical waves. Further detailed analysis of the potentially stereotyped spatio-temporal relationships between individual waves at multiple timescales of interest is necessary to understand the precise coordination of various neuronal circuits in different brain states.