This chapter on Generative AI Foundations provides a comprehensive overview of the key workflow architectures, computational efficiency considerations, and foundational algorithms used in the design and application of generative models. It begins by examining core algorithms and architectures such as Generative Adversarial Networks (GANs), Variational Autoencoders (VAEs), autoregressive models, normalizing flows, and diffusion models, highlighting their unique mechanisms and use cases in tasks like image and text generation. The chapter then addresses computational efficiency challenges, including model complexity, memory optimization, inference speed, and the impact of hardware on training and deployment, offering strategies like mixed precision training, distributed computing, and model pruning to improve performance. It further explores various workflow architectures such as fine-tuning large language models (LLMs) for task-specific adaptation, retrieval-augmented generation (RAG) for combining retrieval with generative models, and prompt engineering, which leverages pre-trained models through task-specific prompts. Finally, the chapter delves into the use of foundation models and end-to-end generative pipelines, illustrating how these models and architectures can be integrated to solve complex, multi-stage tasks across diverse applications, providing both practitioners and research scholars with a foundational understanding of generative AI's capabilities and challenges.