Complex plasma is a rapidly developing area of multidisciplinary world-wide research which is at the frontier of plasma physics where the richness of the complex system approach finds a natural application. Collective phenomena in complex plasma systems, especially related to formation of strongly correlated structures such as dust-plasma crystals attract particular attention since they are often observed in experiments and allow theoretical treatment at the fundamental level of complex system studies. This presentation is focused on physical understanding of the most recent developments in the experiment and theory of self-organized complex structures composed of micrometer-scale dust particles in a plasma. Nowadays, such structures play an important role in complex system science; investigation of their properties gives insights into the basic physics of self-organization in various complex media.
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