This section of the book "A Second Course in Stochastic Processes" by Samuel Karlin and Howard M. Taylor provides an overview of the content and structure of the chapter on "Sums of Independent Random Variables as a Markov Chain." The chapter covers several key topics: 1. **Recurrence Properties of Sums of Independent Random Variables**: Discusses the properties of sums of independent random variables in the context of Markov chains. 2. **Local Limit Theorems**: Explains local limit theorems and their applications. 3. **Right Regular Sequences for the Markov Chain $\{S_{n}\}$**: Introduces the concept of right regular sequences in the Markov chain. 4. **The Discrete Renewal Theorem**: Provides a theorem related to discrete renewal processes. The chapter includes elementary problems, problems for further exploration, notes, and references to support the theoretical discussions.This section of the book "A Second Course in Stochastic Processes" by Samuel Karlin and Howard M. Taylor provides an overview of the content and structure of the chapter on "Sums of Independent Random Variables as a Markov Chain." The chapter covers several key topics: 1. **Recurrence Properties of Sums of Independent Random Variables**: Discusses the properties of sums of independent random variables in the context of Markov chains. 2. **Local Limit Theorems**: Explains local limit theorems and their applications. 3. **Right Regular Sequences for the Markov Chain $\{S_{n}\}$**: Introduces the concept of right regular sequences in the Markov chain. 4. **The Discrete Renewal Theorem**: Provides a theorem related to discrete renewal processes. The chapter includes elementary problems, problems for further exploration, notes, and references to support the theoretical discussions.