From game-playing agents to Large Language Models, Reinforcement Learning (RL) has become the engine behind many of the most significant breakthroughs in modern AI. This course provides a rigorous introduction to the mathematical foundations of algorithmic decision-making, moving from multi-armed bandits to reinforcement learning and concluding with special topics on how these principles are applied at scale to AI models and complex high-dimensional problems like robotics.  Through a mixture of mathematical analysis and algorithmic implementation, students will gain the tools to both understand and develop the next generation of decision-making agents. The course expects students to be comfortable with probability, linear algebra, and basic optimization.