This chapter introduces the concepts of measure theory and probability, emphasizing their importance in statistical inference. While the book does not delve deeply into these topics, a basic understanding is beneficial for several reasons: it simplifies notation, allows for the merging of results for discrete and continuous random variables, handles applications involving censoring or truncation, and is essential for stating many results correctly. The chapter covers the definition of measures, including the counting measure and Lebesgue measure, and discusses the properties of $\sigma$-fields and measures. It also introduces the concepts of finite and $\sigma$-finite measures, with all measures considered in the book being $\sigma$-finite.This chapter introduces the concepts of measure theory and probability, emphasizing their importance in statistical inference. While the book does not delve deeply into these topics, a basic understanding is beneficial for several reasons: it simplifies notation, allows for the merging of results for discrete and continuous random variables, handles applications involving censoring or truncation, and is essential for stating many results correctly. The chapter covers the definition of measures, including the counting measure and Lebesgue measure, and discusses the properties of $\sigma$-fields and measures. It also introduces the concepts of finite and $\sigma$-finite measures, with all measures considered in the book being $\sigma$-finite.