Explore the intricacies of ergodicity in smooth dynamics through this advanced lecture delivered by Jana Rodriguez-Hertz and Amie Wilkinson as part of the Summer School in Dynamics (Introductory and Advanced) series. Delve into complex mathematical concepts and theories related to ergodic systems and their applications in smooth dynamical systems. Gain insights from these expert speakers as they present the fifth installment in this specialized topic, building upon previous lectures and expanding your understanding of ergodic theory in the context of smooth dynamics.