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This chapter presents the principles of Self-Organization, and focuses on Adaptive Resonance Theory (ART) and Self-Organizing Map (SOM) neural networks. It investigates the theoretic basis of formulations of these neural networks, and illustrates a few examples. The structures of these networks and their learning algorithms are also thoroughly explored in the chapter. The ART architecture is a specifically designed neural network to overcome the stability-plasticity dilemma. It is described using nonlinear differential equations. In addition to ART and SOM, there are two other fixed approaches that could be considered fundamental, namely, Neural Gas and the Hierarchical Feature Map. While both are strongly related to the SOM in terms of the learning mechanism, they each have spawned a range of newer architectures are introduced in the chapter. The chapter explains other popular architectures to have emerged based on similar principles of Self-Organization, drawing a distinction between static and dynamic architectures.