Explore the intricacies of Markov partitions for hyperbolic systems with singularities in this comprehensive lecture by Jianyu Chen from Soochow University, China. Delve into key concepts such as scatters, collision maps, uniform hyperbolicity, and the structure of singularities. Examine the union of singularities, asylum, SRB measures, and one-step expansion. Gain insights into coupling and perfect property through a detailed proof. Engage with a brief overview and participate in a question-and-answer session to deepen your understanding of this complex mathematical topic.