This chapter introduces measure theory and probability, and states several important results without proof. The book does not treat probability and measure theory with rigor, but some basic knowledge is useful for understanding statistical inference and the literature in statistics. The notation of measure theory allows merging results for discrete and continuous random variables and handles applications involving censoring or truncation. The language of measure theory is necessary for stating many results correctly. A measure μ on a set X assigns a nonnegative value μ(A) to many subsets A of X. For example, counting measure assigns the number of points in a set, while Lebesgue measure assigns the length, area, or volume of a set in R^n. These measures differ in that counting measure assigns mass to individual points, while Lebesgue measure assigns zero mass to isolated points. A measure is defined on a σ-field, which is a collection of subsets of X that satisfies certain properties. A function μ on a σ-field A of X is a measure if it assigns a nonnegative value to each set in A and satisfies the property that the measure of the union of disjoint sets is equal to the sum of their measures. This property leads to a continuity property of measures. A measure is finite if its total measure is finite, and σ-finite if the entire space can be covered by a countable collection of sets with finite measure. All measures considered in this book are σ-finite.This chapter introduces measure theory and probability, and states several important results without proof. The book does not treat probability and measure theory with rigor, but some basic knowledge is useful for understanding statistical inference and the literature in statistics. The notation of measure theory allows merging results for discrete and continuous random variables and handles applications involving censoring or truncation. The language of measure theory is necessary for stating many results correctly. A measure μ on a set X assigns a nonnegative value μ(A) to many subsets A of X. For example, counting measure assigns the number of points in a set, while Lebesgue measure assigns the length, area, or volume of a set in R^n. These measures differ in that counting measure assigns mass to individual points, while Lebesgue measure assigns zero mass to isolated points. A measure is defined on a σ-field, which is a collection of subsets of X that satisfies certain properties. A function μ on a σ-field A of X is a measure if it assigns a nonnegative value to each set in A and satisfies the property that the measure of the union of disjoint sets is equal to the sum of their measures. This property leads to a continuity property of measures. A measure is finite if its total measure is finite, and σ-finite if the entire space can be covered by a countable collection of sets with finite measure. All measures considered in this book are σ-finite.