The brain is a complex system involving multitudinous neuron- and receptor types and evolved connectivity that compose an intricate functional architecture. At the collective level, this system produces ubiquitous oscillations that are -to some degree- specific of their originating circuits. I will first follow the state of the art in electrophysiology of awake human subjects. I will show how to distinguish brain processes that are closely related in the spatial and spectral domains. This approach effectively isolates distinct brain rhythms and improves the measure of their respective contribution. I will illustrate this approach with a recent study of interpersonal coordination dynamics that revealed a neuromarker of social behavior in the 10Hz band. However, understanding the parts is not the whole story. Because of emergence and self-organization, we crucially need another level of explanation: how brain parts work together (or constrain each other) to achieve harmonious functioning. This can be understood in the framework of non-linear dynamical systems. I will first introduce a theoretical model of coordination dynamics. Next, to gain access to the expectations of the model in real EEG, I will compute forward models of various sources dynamics and underline key properties that reveal the underlying cortical organization. These signatures are to be targeted in EEG signals. Finally, I will present some episodes of EEG that illustrate the concepts of independence, recruitment, phase-synchronization and metastability. In conclusion, I will stress the limitations of current methods of EEG analysis to speak of cortical source dynamics and I will briefly sketch future directions. [PPT].