Delve into the intricacies of axion theory in this comprehensive lecture focusing on the low energy Lagrangian. Explore fundamental concepts and advanced theoretical frameworks as presented by Giovanni Villadoro at the Galileo Galilei Institute. Over the course of 1 hour and 36 minutes, gain a deep understanding of axion physics and its implications in modern particle theory. Engage with complex mathematical formulations and physical interpretations that form the backbone of this cutting-edge research area. Ideal for graduate students, researchers, and professionals in theoretical physics seeking to expand their knowledge of axion theory and its applications in contemporary physics.