The chapter introduces the concept of differential privacy, a robust and mathematically rigorous definition of privacy tailored for privacy-preserving data analysis. It emphasizes the importance of a strong privacy guarantee that can protect individuals from any additional harm due to their data being included in a database, even if the harm is not directly observed. The chapter discusses the limitations of other approaches to privacy, such as anonymization and summary statistics, which can be vulnerable to linkage attacks and reconstruction attacks. The formal definition of differential privacy is presented, along with key properties and implications. Differential privacy ensures that the behavior of an algorithm remains roughly unchanged even if a single entry in the database is modified. This property, known as "granularity," allows for flexible privacy guarantees depending on the context and sensitivity of the data. The chapter also highlights the importance of quantifying privacy loss, composing multiple differentially private mechanisms, and ensuring group privacy. The chapter concludes by discussing the economic and utility-theoretic aspects of differential privacy, emphasizing that it does not promise unconditional freedom from harm but rather aims to minimize the risk of harm to individuals. It also addresses the limitations of differential privacy, such as its inability to create privacy where none previously existed, and the need for careful scrutiny of privacy claims to understand the level of granularity at which privacy is being promised.The chapter introduces the concept of differential privacy, a robust and mathematically rigorous definition of privacy tailored for privacy-preserving data analysis. It emphasizes the importance of a strong privacy guarantee that can protect individuals from any additional harm due to their data being included in a database, even if the harm is not directly observed. The chapter discusses the limitations of other approaches to privacy, such as anonymization and summary statistics, which can be vulnerable to linkage attacks and reconstruction attacks. The formal definition of differential privacy is presented, along with key properties and implications. Differential privacy ensures that the behavior of an algorithm remains roughly unchanged even if a single entry in the database is modified. This property, known as "granularity," allows for flexible privacy guarantees depending on the context and sensitivity of the data. The chapter also highlights the importance of quantifying privacy loss, composing multiple differentially private mechanisms, and ensuring group privacy. The chapter concludes by discussing the economic and utility-theoretic aspects of differential privacy, emphasizing that it does not promise unconditional freedom from harm but rather aims to minimize the risk of harm to individuals. It also addresses the limitations of differential privacy, such as its inability to create privacy where none previously existed, and the need for careful scrutiny of privacy claims to understand the level of granularity at which privacy is being promised.