This lecture covers the concepts of policy gradient and actor-critic methods in reinforcement learning, focusing on eligibility traces. The instructor begins by introducing eligibility traces and their natural emergence within the policy gradient framework. A distinction is made between episodic and continuing environments, emphasizing the optimization of returns from all states rather than just a single starting state. The lecture progresses through mathematical formulations, demonstrating how to optimize expected returns over multiple time steps. The instructor explains the significance of eligibility traces in updating parameters and introduces shadow variables for effective learning. The application of these concepts is illustrated through a maze navigation task, showcasing the advantages of actor-critic methods with eligibility traces over traditional reinforcement learning approaches. The lecture concludes with a discussion on model-based versus model-free reinforcement learning, highlighting the benefits of having a model of the environment for adaptability and planning. Overall, the lecture provides a comprehensive understanding of advanced reinforcement learning techniques and their practical implications.