This course provides a hands-on introduction to large language models and generative AI. Students will learn how modern AI systems work, from the transformer architecture and training process through to practical applications including retrieval-augmented generation, tool use, and AI agents. Topics include LLM APIs and prompting, chain-of-thought reasoning, function calling, embeddings and vector search, RAG pipelines, the ReAct agent paradigm, fine-tuning and RLHF, large reasoning models, and multimodal AI. The course emphasizes both conceptual understanding and practical skills through five programming assignments.