Explore the third lecture in a five-part series on symbolic dynamics for nonuniformly hyperbolic systems. Delve into advanced concepts in dynamical systems theory, including Markov partitions and Young towers. Learn about the groundbreaking work of Sinai, Ruelle, and Bowen in applying ergodic theory to differentiable dynamical systems. Examine the challenges of extending these results to nonuniformly hyperbolic systems and the development of infinite Markov partitions. Gain insights into the construction of SRB measures and their statistical properties. Cover key topics such as Catoc, neighborhood theorems, and absolute overlap in the context of symbolic dynamics. This lecture, part of a mini-course on Markov Partitions and Young Towers in Dynamics, is designed for those with some familiarity in uniformly hyperbolic dynamics.