To effectively build upon Generative Adversarial Networks, we first solidify our understanding of the core principles. This chapter provides a focused review of the foundational concepts essential for tackling more complex GANs.

We will re-examine:

• The fundamental roles and interaction of the Generator and Discriminator networks.
• The original minimax objective function, often expressed as $\min_G \max_D V(D, G)$, and its theoretical basis.
• Common training instabilities, such as mode collapse and vanishing gradients, that can hinder convergence.
• The inherent limitations of the initial GAN formulation, motivating the need for advanced techniques.
• A brief refresher on the architectural improvements introduced by Deep Convolutional GANs (DCGANs).

This review establishes a common ground, ensuring clarity on the basic mechanics and challenges before proceeding to advanced architectures and stabilization methods.