This chapter examines the mathematical foundations of generative models, key components of modern machine learning (ML) and artificial intelligence (AI). Generative models are algorithms designed to replicate complex patterns in data by generating new samples that resemble the original dataset. This chapter reviews the essential concepts in probability theory, such as conditional probability, probability distributions, and Bayes’ theorem, which are fundamental to understanding generative modeling. This chapter also explores core techniques in generative modeling, including probabilistic graphical models like Markov random fields and Bayesian networks, which provide structured frameworks for representing relationships between variables. The chapter also examines deep generative models, which utilize deep neural networks to learn hierarchical data representations, enabling the creation of highly accurate examples. Further, this chapter also discusses the importance of loss functions in guiding the learning process and evaluating the quality of generated data. The chapter also covers the mathematical principles behind neural networks, using linear algebra and calculus to explain how these networks learn and make predictions. Ultimately, this chapter equips readers with a solid understanding of the mathematical underpinnings of generative models, enabling them to develop innovative algorithms for applications like text generation, drug discovery, and image synthesis.